Find the Quadratic Polynomial Whose zeros are 3 and -4

Answer: Let’s denote the quadratic polynomial as ax² + bx + c = 0, where a≠0 and the zeroes as α and β. Here, α = -3 and β = 4.

To find the quadratic polynomial in terms of the zeroes α and β, we need to apply the following formula:-

p(x) = x² – (sum of zeroes) x + product of zeroes

Sum of the zeroes = α + β = -3 + 4 = 1 ……….eq (i)

Product of the zeroes = α * β = -3 * 4 = -12 ……….eq (ii)

Now, substitute the computed values of eq (i) and eq (ii) in the following formula:-

p(x) = x² – (α + β)x + αβ

p(x) = x² – (1) x + (-12)

p(x) = x² – x – 12

Therefore, the quadratic polynomial whose zeros are 3 and – 4 is x² – x – 12.