Question

Find a quadratic polynomial whose zeroes are -3 and 4.

Answer 1

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Answer 2

Given that,

Zeroes of a quadratic polynomial are -3 and 4.

To find,

A quadratic equation.

Solution,

The general form of a quadratic equation is given by :

$ax^2+bx+c$

or

$x^2+(\text{sum of zeroes})x+\text{product of zeroes}$

If $\alpha$ and $\beta$ are the roots of a quadratic equation then,

$x^2+(\alpha+\beta )x+\alpha\beta$

Sum of zeroes, -3+4 = 1

Product of zeroes, (-3)(4) = -12

So, the quadratic polynomial is :

$x^2-x-12$

Hence, this is the required solution.