Question

If - √5 and √5 are the roots of the quadratic polynomial. Find the quadratic polynomial.

i) x - 5
ii) (x - 5) ( x + 5 )
iii) x² - 5
iv) x² - 25​

Answer 1

Answer:

option (iii) x² - 5

Step-by-step explanation:

Given :

-√5 and √5 are the roots of the quadratic polynomial

To find :

the quadratic polynomial

Solution :

Let the roots be α and β

• α = -√5

• β = √5

Sum of roots = α + β

   = -√5 + √5

   = 0

Product of roots = αβ

   = (-√5) × (√5)

   = -(√5)²

   = -5

The quadratic polynomial is of the form

 x² - (sum of the roots)x + (product of the roots)

⇒ x² - (α + β)x + αβ

⇒ x² - (0)x + (-5)

⇒ x² - 0 - 5

⇒ x² - 5

∴ The required polynomial is x² - 5