Question

5 root 5x^2 + 30x + 8 root 5 find the zeroes of the polynomial

Answer 1

Answer:

Zeroes of the polynomial are $\frac{-2\sqrt{5} }{5}$ , $\frac{-4\sqrt{5} }{5}$

Step-by-step explanation:

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 = $\frac{-2\sqrt{5} }{5}$

Also,

√5 x + 4 = 0

√5 x = - 4

x = $\frac{-4}{\sqrt{5} }$

Multiplying and dividing by √5

x = $\frac{-4}{\sqrt{5} } *\frac{\sqrt{5} }{ \sqrt{5} }$

x = $\frac{-4\sqrt{5} }{5}$

Hence,

Zeroes of the polynomial are $\frac{-2\sqrt{5} }{5}$ , $\frac{-4\sqrt{5} }{5}$

Answer 2

Answer:

5√5x² + 30x + 8√5

splitting the middle term

= 5√5x² + 20x + 10x + 8√5

= 5√5x² + 4 × 5x + (2√5 ) × √5 x + 2√5 × 4

= 5x ( √5x + 4 ) + ( 2√5 ) [ √5x + 4 ]

= ( √5x + 4 ) ( 5x + 2√5 )