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Solved Examples
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DD  Without graphing, find out how many x-intercepts the given function has.
y = 0.8x2 + 8x + 20  DD
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DD  Solve the following equation using the quadratic formula.
- x2 + 5x - 8 = 0
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DD  Solve the following equation using the quadratic formula.
x2 + 9x + 8 = 0  DD
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DD  Solve the following equation using the quadratic formula.
x2 = 9x - 4
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DD  Solve the following equation using the quadratic formula.
x2 + 2x - 4 = 0  DD
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DD  Solve the following equation using the quadratic formula.
x2 = 12x - 40
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DD  Solve the following equation using the quadratic formula.
x2 - 8x + 18 = 0
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DD  Solve the equation using quadratic formula.
(x + 9)19 = 9(x + 8)
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DD  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  DD
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DD  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  DD
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DD  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
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DD  Calculate the value of m if 49x2 + mx + 64 = 0 has one real solution.  DD View Solution
DD  Calculate the value of p if x2 + 10x + p = 0 has one real solution.  DD View Solution
DD  Form a quadratic equation to find the area of a square that has area equal to the area as the circle shown. [a = 13.]
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DD  Without graphing, find out how many x-intercepts the given function has.
y = x2 + 6 - 11(x + 5)
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DD  Frame a quadratic equation in x, whose solutions are - 6 ± 6i.
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DD  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?  DD View Solution
DD  Calculate the value of m if 9x2 + mx + 9 = 0 has two real solutions.
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DD  Calculate the value of m if 4x2 + mx + 25 = 0 has two imaginary solutions.
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DD  Solve the following equation using the quadratic formula.
x2 = 8x - 20
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DD  Solve the following equation using the quadratic formula.
x2 - 4x + 9 = 0
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DD  Solve the equation using quadratic formula.
(x + 6)13 = 6(x + 5)
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DD  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
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DD  Calculate the value of m if 16x2 + mx + 25 = 0 has one real solution.  DD View Solution
DD  Calculate the value of p if x2 + 6x + p = 0 has one real solution.  DD View Solution
DD  Without graphing, find out how many x-intercepts the given function has.
y = x2 + 5 - 10(x + 2)
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DD  Calculate the value of m if 25x2 + mx + 25 = 0 has two real solutions.
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DD  Solve the following equation using the quadratic formula.
x2 + 12x - 10 = 0  DD
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DD  Solve the following equation using the quadratic formula.
x2 = 6x - 13
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DD  Solve the following equation using the quadratic formula.
x2 - 4x + 15 = 0
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DD  Solve the equation using quadratic formula.
(x + 5)11 = 5(x + 4)
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DD  Match the function with its graph, using the discriminant y = 2x2 + 4x + 3.
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DD  Match the function with its graph, using the discriminant y = 2x2 - 4x + 2.
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DD  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  DD
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DD  Solve the following equation using the quadratic formula.
x2 + 5x + 4 = 0  DD
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DD  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  DD
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DD  Match the function with its graph, using the discriminant y = 4x2 - 2.
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DD  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
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DD  Calculate the value of m if 4x2 + mx + 9 = 0 has one real solution.  DD View Solution
DD  Solve the following equation using the quadratic formula.
- x2 + 3x - 5 = 0
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DD  Calculate the value of p if x2 + 8x + p = 0 has one real solution.  DD View Solution
DD  Solve the following equation using the quadratic formula.
x2 = 11x - 5
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DD  Form a quadratic equation to find the area of a square that has area equal to the area as the circle shown. [a = 8.]
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DD  Without graphing, find out how many x-intercepts the given function has.
y = x2 + 8 - 11(x + 2)
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DD  Frame a quadratic equation in x, whose solutions are - 8 ± 2i.
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DD  The area of a rectangle is 64 cm2 and its perimeter if 64 cm. Find the dimensions of the rectangle to the nearest hundredth.  DD View Solution
DD  The number of quadratic equations which are unaltered by the squaring of their roots is
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DD  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?  DD View Solution
DD  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 ________
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DD  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?  DD View Solution
DD  Check if the statement is true or false.
"A quadratic equation with real coefficients cannot have exactly one imaginary root."
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DD  Calculate the value of m if 36x2 + mx + 9 = 0 has two real solutions.
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DD  Calculate the value of m if 4x2 + mx + 4 = 0 has two imaginary solutions.
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DD  If one of the root of 9x2 + 19x + k = 0 is the reciprocal of the other then k = ______  DD View Solution
DD  Both the roots of the equation (x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 are always _________
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DD  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 ______
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DD  The number of roots of the equation 4 + x - 2 = x is ________  DD View Solution