Find a quadratic polynomial whose zeros are - 4 and 2?

Answer: +2x8

Let the assume quadratic polynomial be ax²+bx+c=0, where a≠0 and it’s zeroes be α and β.

Here

α = -4

β = 2

We know that

(1) Sum of the zeroes

⇒ α + β

⇒ -4 + 2

⇒ -2……………………………(1)

(2) Product of the zeroes

⇒ α × β

⇒ -4 × 2

⇒ -8……………………………(2)

∴ The quadratic polynomial ax²+bx+c is k[x2 + (α + β)x + αβ]

Where k is constant.

k[x2 + (α + β)x + αβ]

From equation (1) and (2) we get

⇒ k[x2 -2x -8]

When k = 1 the quadratic equation will become

x2 -2x -8

Leave a Comment

Your email address will not be published. Required fields are marked *

BOOK

Free Class