Answer :

given polynomial is

5√5x^{2} + 30x + 8√5

Now factorizing by splitting the middle term.

Now we need to find two numbers whose sum is 30 and

Product is 5√5 × 8√5 = 5 × 8 × √5 × √5 = 40 × 5 = 200

So, the above given polynomial is

5√5x^{2} + 20x + 10x + 8√5

= 5√5x^{2} + 20x + (5 × 2) x + 8√5

= 5√5x^{2} + 20x + (√5 × √5 × 2) x + 8√5

= 5x (√5x + 4) + 2√5(√5x + 4)

= (5x + 2√5) (√5x + 4)

So, the zeroes of the polynomial will be

5x + 2√5 = 0 and √5x + 4 = 0

⇒ 5x = - 2√5 and √5x = - 4

Hence the zeroes of the given polynomial are and .

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