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A quadratic polynomial, whose zeroes are $- 3$ and $4$ is

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\frac{x^{2}}{2} - \frac{x}{2} - 6

x^{2} - x - 12

x^{2} - x

x^{2} - x - 6

answer is C.

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Detailed Solution

Given, the zeroes pf the quadratic polynomial are -3 and 4.
We need to find the quadratic respective quadratic equation.
Quadratic equation with

α

and

β

as roots can be written as

x^{2} - (α + β) x + αβ = 0

Here,

α = - 3

and

β = 4

∴ α + β = - 3 + 4 = 1

and

α - β = - 3 \times 4 = - 12

∴

The quadratic equation is

x^{2} - (α + β) x + αβ = 0

\Rightarrow x^{2} - 1 x - 12 = 0

\Rightarrow \frac{x^{2}}{2} - \frac{x}{2} - \frac{12}{2} = 0

\Rightarrow \frac{x^{2}}{2} - \frac{x}{2} - 6 = 0

Thus, the quadratic polynomial is

\frac{x^{2}}{2} - \frac{x}{2} - 6 .

Hence, the correct option is 3.

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