Find the quadratic polynomial, whose zeroes are − 3 and 4.

We are given the zeros of a quadratic polynomial, and we must find the polynomial.

The general polynomial, which can be formed using zeroes, can be written as:

𝑥² + (𝑠𝑢𝑚 𝑜𝑓 𝑧𝑒𝑟𝑜𝑒𝑠)𝑥 + (𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑧𝑒𝑟𝑜𝑒𝑠) = 0

So, if we find the sum and product of the zeroes, we can find the polynomial. The two zeroes of the polynomial are − 3 and 4.

The sum of the zeroes =− 3 + 4

⇒ 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑧𝑒𝑟𝑜𝑒𝑠 = 1

And the product of zeroes =− 3 × 4

⇒ 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑧𝑒𝑟𝑜𝑒𝑠 =   − 12

So, the polynomial is given by,

𝑥² + 1𝑥 + (− 12) = 0

⇒ 𝑥² + 𝑥 − 12 = 0

This is the required quadratic polynomial.