Question

For each of the following, find a quadratic polynomial whose sum and

product respectively of the zeroes are as given. Also, find the zeroes of

these polynomial by factorization.
i) -1/3 , 1

ii) 0 , -9
​

Answer 1

Answer:

(i) 3x² + x + 3

(ii) x² - 9

Step-by-step explanation:

Question (i) :

Given -

• Sum of zeroes = - 1/3
• Product of zeroes = 1

We know that, the zeroes of the quadratic polynomial are α and β, and the quadratic polynomial so formed is in the form of ;

x² - (α + β)x + αβ

So, the required polynomial is -

⇒ x² - (sum of zeroes)x + product of zeroes

⇒ x² - ( $\dfrac{-1}{3}$ ) x + 1

⇒ x² + $\dfrac{1}{3}$ x + 1

⇒ $\sf \dfrac{3x^2 + x + 3}{3}$ = 0

⇒ 3x² + x + 3 = 0

Hence, the required quadratic polynomial is 3x² + x + 3.

_______________________

Question (ii) :

Given -

• Sum of zeroes = 0
• Product of zeroes = - 9

We know that, the zeroes of the quadratic polynomial are α and β, and the quadratic polynomial so formed is in the form of ;

x² - (α + β)x + αβ

So, the required polynomial is -

⇒ x² - (sum of zeroes)x + product of zeroes

⇒ x² - 0x + (-9)

⇒ x² - 9

Hence, the required quadratic polynomial is x² - 9.