Question

I will mark u brilliant...

If a and ß are the zeroes of a quadratic polynomial such that a + ß = 0 and a- ß = 8. Find the quadratic polynomial having a and ß as it's zeroes.
Plz answer me fast.

Answer 1

Answer:

x² - 16

Step-by-step explanation:

Given that α and β are the zeros of a quadratic polynomial such that

α + β = 0

α - β = 8

----------------

2α = 8

α = 4

Substitute α = 4 in (1), we get

α + β = 0

⇒ 4 + β = 0

⇒ β = -4

The value of α and β are 4 and -4 respectively.

If α and β are the zeros of a quadratic polynomial, the polynomial is in the form of

P(x) = x² - (α + β)x + αβ

     = x² - 0 - 16

    = x² - 16

Therefore, the required polynomial is x² - 16

Hope it helps!