Find a Quadratic Polynomial Whose Zeroes are -4 and 2
A quadratic polynomial is of the form f(x) = ax2+bx+c and a ≠ 0
Answer: x2 + 2x - 8 is the Quadratic Polynomial Whose zeroes are -4 and 2
Let us see, how to solve.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 - (sum of the zeroes) x + (product of the zeroes)
f(x) = x2 - (α +β) x +αβ
Given that zeroes of a quadratic polynomial are -4 and 2
let α = -4 and β= 2
Therefore, substituting the value α = -4 and β= 2 we get
f(x) = x2 - (α + β) x + αβ
= x2 - ( -4 + 2) x +(-4)(2)
= x2 + 2x - 8
Thus, x2 + 2x - 8 is the quadratic polynomial whose zeroes are -4 and 2.