Find a Quadratic Polynomial Whose Zeroes are -3 and 4
A quadratic polynomial is of the form f(x) = ax2+bx+c and a ≠ 0
Answer: x2 - x - 12 is the Quadratic Polynomial Whose zeroes are -3 and 4
Let us see, how to solve it.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 -(sum of the zeroes) x + (product of the zeroes)
i.e, f(x) = x2 -(α +β) x +αβ
Given that zeroes of a quadratic polynomial are -3 and 4
Let α = -3 and β= 4
Therefore, substituting the value α = -3 and β= 4 inf(x) = x2 -(α +β) x +αβ, we get
f(x) = x2 - ( -3 + 4) x +(-3)(4)
= x2 - x -12
Thus, x2 - x -12 is the quadratic polynomial whose zeroes are -3 and 4.