Question

20. A quadratic polynomial, the sum of
whose zeroes is zero and one zero is
4, is ...
A) x2 – 16
B) x2 + 16
C) x2 - 4
D) x2 + 4​

Answer 1

Given :

• Sum of zeroes of the polynomial = 0.

• One of the zeroes of the polynomial = 4.

To find :

The Quadratic polynomial .

Solution :

Let the first zero of the polynomial be α and the second zero of the polynomial be β.

Here according to the given information ,

• α = 4

According to the Question ,

Sum of zeroes of the polynomial = 0.

==> α + β = 0

==> 4 + β = 0

==> β = 0 - 4

∴ β = -4

Hence the second zero of the polynomial is -4.

Now to find out Quadratic equation,

We know the formula for Quadratic equation when the zeroes are given.i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀x² + (α + β)x + αβ

Now Substituting the values in it , we get :

==> x² + (α + β)x + αβ

==> x² + [4 + (-4)}x + 4 × (-4)

==> x² + (4 - 4)x + (-16)

==> x² + (0)x - 16

==> x² + 0 - 16

==> x² - 16.

∴ x² - 16 = 0

Hence the Quadratic equation is x² - 16.