Question

Find the zeroes of the following, quadratic
polynomial and verify the relationship between
zeroes and the coeffiecient f(x) = 5 √5 x^2 + 30x+8√5​

Answer 1

Answer:

Zeroes of the polynomial are -2√5/5 , -4√5/5

Given equation,

5 root 5x^2 + 30x + 8 root 5

This can be written as ,

5√5 x² + 30 x + 8√5

We will factorise the given equation by splitting the middle term method

5√5 x² + 20 x + 10 x + 8√5

10 x can be written as ( 5×2 ) x

5√5 x² + 20 x + ( 5 ×2 ) x + 8√5

Also, 5 can be written as √5 × √5

So now the Equation becomes :

= 5√5 x² + 20 x + ( √5 ×√5 ×2 ) x + 8√5

= 5x ( √5 x + 4 ) + √5 ×2 ( √5 x + 4 )

= 5x ( √5 x + 4 ) + 2√5 ( √5 x + 4 )

= ( 5x + 2√5 ) ( √5 x + 4 )

Zeroes are :

5x + 2√5 = 0

5x = - 2√5

x = -2√5/5

Also,

√5 x + 4 = 0

√5 x = - 4

x = -4/√5

Multiplying and dividing by √5

x = -4√5/5

Hence,

Zeroes of the polynomial are -2√5/5 , -4√5/5

Hope it helps!

(pls mark it the brainliest^^)

Step-by-step explanation: