Question

LEt f(x) be a quadratic polynomial such that f(2)=-3 and f(-2)=21. Then the coefficient of x in f(x) is???

Answer 1

OK, let's start from the basics!\[f(x)= ax^2 + bx \]And so, this way\[f(2) = -3 \Rightarrow 4a + 2b=-3 \]\[f(-2) = 21 \Rightarrow 4a-2b = 21\]

Answer 2

(x-a)(x-b) = x^2 - abx + ab.

Answer 3

These are the two equations you have. Solve them.

Answer 4

@primeralph that should be \[(x-a)(x+b) = x^2 - ax -bx +ab = x^2 -(a+b)x + ab\]

Answer 5

Yes. True.