Asked Nov 5, 2019

Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=18

check_circleExpert Solution
Step 1

zeros are  -3,-1, and 4.

So factors are (x+3), (x+1) and (x-4). [when x=k is a zero then (x-k) is a factor]

Step 2

Let the polynomial is f(x)=a(x+3)(x+1)(x-4)

Given f...

f(x) a(x+3)(x+1)(x-4)
f(-2) a(-2+3)-2+1)(-2-4)
18 a(1) 6

Image Transcriptionclose

f(x) a(x+3)(x+1)(x-4) f(-2) a(-2+3)-2+1)(-2-4) 18 a(1) 6 18-6a 18 6 a=3


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