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Solved Examples
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c   Without graphing, find out how many x-intercepts the given function has.
y = 0.8x2 + 8x + 20   c
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c   Solve the following equation using the quadratic formula.
- x2 + 5x - 8 = 0
   c
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c   Solve the following equation using the quadratic formula.
x2 + 9x + 8 = 0   c
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c   Solve the following equation using the quadratic formula.
x2 = 9x - 4
   c
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c   Solve the following equation using the quadratic formula.
x2 + 2x - 4 = 0   c
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c   Solve the following equation using the quadratic formula.
x2 = 12x - 40
   c
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c   Solve the following equation using the quadratic formula.
x2 - 8x + 18 = 0
   c
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c   Solve the equation using quadratic formula.
(x + 9)19 = 9(x + 8)
   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
9x2 - 5x + 8 = 0   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
9x2 + 17x - 6 = 0   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
4x2 + 12x + 9 = 0
   c
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c   Calculate the value of m if 49x2 + mx + 64 = 0 has one real solution.   c View Solution
c   Calculate the value of p if x2 + 10x + p = 0 has one real solution.   c View Solution
c   Form a quadratic equation to find the area of a square that has area equal to the area as the circle shown. [a = 13.]
   c
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c   Without graphing, find out how many x-intercepts the given function has.
y = x2 + 6 - 11(x + 5)
   c
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c   Frame a quadratic equation in x, whose solutions are - 6 ± 6i.
   c
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c   Joe throws a stick straight up in the air from the ground. The function h = - 14t2 + 42t models the height h (in feet) of the stick above the ground after t seconds. Will the stick ever reach a height of 21 ft?   c View Solution
c   Calculate the value of m if 9x2 + mx + 9 = 0 has two real solutions.
   c
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c   Calculate the value of m if 4x2 + mx + 25 = 0 has two imaginary solutions.
   c
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c   Solve the following equation using the quadratic formula.
x2 = 8x - 20
   c
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c   Solve the following equation using the quadratic formula.
x2 - 4x + 9 = 0
   c
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c   Solve the equation using quadratic formula.
(x + 6)13 = 6(x + 5)
   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
36x2 + 132x + 121 = 0
   c
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c   Calculate the value of m if 16x2 + mx + 25 = 0 has one real solution.   c View Solution
c   Calculate the value of p if x2 + 6x + p = 0 has one real solution.   c View Solution
c   Without graphing, find out how many x-intercepts the given function has.
y = x2 + 5 - 10(x + 2)
   c
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c   Calculate the value of m if 25x2 + mx + 25 = 0 has two real solutions.
   c
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c   Solve the following equation using the quadratic formula.
x2 + 12x - 10 = 0   c
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c   Solve the following equation using the quadratic formula.
x2 = 6x - 13
   c
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c   Solve the following equation using the quadratic formula.
x2 - 4x + 15 = 0
   c
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c   Solve the equation using quadratic formula.
(x + 5)11 = 5(x + 4)
   c
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c   Match the function with its graph, using the discriminant y = 2x2 + 4x + 3.
   c
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c   Match the function with its graph, using the discriminant y = 2x2 - 4x + 2.
   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
5x2 - 5x + 4 = 0   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
7x2 + 13x - 5 = 0   c
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c   Use the discriminant of the given function to predict how many solutions it has. Also check if the solutions are real or imaginary.
16x2 + 56x + 49 = 0
   c
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c   Calculate the value of m if 4x2 + mx + 9 = 0 has one real solution.   c View Solution
c   Calculate the value of p if x2 + 8x + p = 0 has one real solution.   c View Solution
c   Form a quadratic equation to find the area of a square that has area equal to the area as the circle shown. [a = 8.]
   c
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c   Without graphing, find out how many x-intercepts the given function has.
y = x2 + 8 - 11(x + 2)
   c
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c   Frame a quadratic equation in x, whose solutions are - 8 ± 2i.
   c
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c   The area of a rectangle is 64 cm2 and its perimeter if 64 cm. Find the dimensions of the rectangle to the nearest hundredth.   c View Solution
c   Ed throws a stick straight up in the air from the ground. The function h = - 20t2 + 70t models the height h (in feet) of the stick above the ground after t seconds. Will the stick ever reach a height of 30 ft?   c View Solution
c   Tim throws a stick straight up in the air from the ground. The function h = - 16t2 + 48t models the height h (in feet) of the stick above the ground after t seconds. How many seconds does it take the stick to reach a height of 24 ft?   c View Solution
c   Solve the following equation using the quadratic formula.
x2 + 5x + 4 = 0   c
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c   Match the function with its graph, using the discriminant y = 4x2 - 2.
   c
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c   Solve the following equation using the quadratic formula.
- x2 + 3x - 5 = 0
   c
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c   Solve the following equation using the quadratic formula.
x2 = 11x - 5
   c
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c   Check if the statement is true or false.
"A quadratic equation with real coefficients cannot have exactly one imaginary root."
   c
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c   Calculate the value of m if 36x2 + mx + 9 = 0 has two real solutions.
   c
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c   Calculate the value of m if 4x2 + mx + 4 = 0 has two imaginary solutions.
   c
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c   The number of quadratic equations which are unaltered by the squaring of their roots is
   c
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c   If α, β are the roots of x2 - 6x + a = 0 and γ, δ are the roots of x2 - 150x + b = 0 and the numbers α, β, γ and δ (in order) form an increasing G.P then ________
   c
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c   If one of the root of 9x2 + 19x + k = 0 is the reciprocal of the other then k = ______   c View Solution
c   Both the roots of the equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are always _________
   c
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c   If the equation k(3x2 + 3) + rx + 4x2 - 8 = 0 and 3k(2x2 + 2) + px + 8x2 - 16 = 0 have both the roots common then the value of 2r - p is ______
   c
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c   The number of roots of the equation 4 + x - 2 = x is ________   c View Solution