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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.
