Attempt following question by selecting a choice to answer.
f
Which of the following is a polynomial of degree 4 with real coefficients that has having zeros
3, - 1, and 2 - i?c fA.
f f (
x) = 2
x4-12x3+20x2 + 4x - 30
B.
ff (
x) =
2x4-12x3-30x2 + 4x - 30
C.
ff (
x) =
2x4-12x3+30x2 + 4x + 30
D.
fnone of the above
f
A
Step 1: The zeros of the function are 3, - 1, and 2 - i.
Step 2: If (2 - i) is a complex zero of a function f (x), then its conjugate complex (2 + i) is also a zero of that function.
Step 3: So, the polynomial function of degree 4 with the given zeros is f (x) = 2(x - 3)(x + 1)[x - (2 - i)][x - (2 + i)]
Step 4: = 2(x2-2x-3)[x2-(2+i)x-(2-i)x+(22-i2)]
Step 5: = 2(x2 - 2x - 3) (x2 - 4x + 5)
Step 6: = 2[x4-4x3+5x2-2x3+8x2-10x-3x2+12x - 15]
Step 7: So, the polynomial function of degree 4 with the given zeros is f (x) = 2x4-12x3+20x2+4x - 30.