Question

x^2- root5-30,Find the zeros of the polynomial and find the Relation between the zeros and its coefficents

Answer 1

Answer:

Given equation,

5 root 5 x square + 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 = -2root5/5

Also,

√5 x + 4 = 0

√5 x = - 4

x = -4/root5

Multiplying and dividing by √5

 x = -4root5/5

Hence,

Zeroes of the polynomial are , -2root5/5, -4root5/5

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