Question

find a quadratic polynomial whose zeroes are 2 and -6.​

Answer 1

Given : Zeroes of a quadratic polynomial are 2 and -6

To Find : The quadratic polynomial.

⠀⠀⠀⠀⠀⠀⠀ ______________

As we know that :

• Quadratic polynomial = x² - (sum of zeroes)x + product of zeroes

=> x² - (α + β)x + αβ

⠀⠀ ⠀⠀⠀⠀ ______________

Firstly, we'll find the sum of zeroes of the quadratic polynomial.

=> sum of zeroes = {2 + (-6)}

=> sum of zeroes = 2 - 6

=> sum of zeroes = -4

Now, we'll find the product of zeroes of the quadratic polynomial.

=> product of zeroes = 2 × (-6)

=> product of zeroes = -12

Now, we'll put the values of sum and product of zeroes in the formula.

=> Quadratic polynomial = x² - (sum of zeroes)x + product of zeroes

=> Quadratic polynomial = x² - (-4)x + (-12)

=> Quadratic polynomial = x² + 4x - 12

∴ Hence, the quadratic polynomial is x² + 4x - 12.