Question

factorize:
$5 \sqrt{5x }^{2} + 30x + 8 \sqrt{5}$
​

Answer 1

SOLUTION:-

Given:

5√5x² +30x +8√5

Therefore,

Factorize by splitting the middle term.

$5 \sqrt{5} {x}^{2} + 30x + 8 \sqrt{5} \\ \\ = > 5 \sqrt{5} {x}^{2} + 20x + 10x + 8 \sqrt{5} = 0 \\ \\ = > 5 \sqrt{5} {x}^{2} + 20x + (5 \times 2)x + 8 \sqrt{5} = 0 \\ \\ = > 5 \sqrt{5} {x}^{2} + 20x + ( \sqrt{5} \times \sqrt{5} \times 2)x + 8 \sqrt{5} = 0 \\ \\ = > 5x( \sqrt{5} x + 4) + \sqrt{5} \times 2( \sqrt{5} x + 4) = 0 \\ \\ = > 5x( \sqrt{5} x + 4) + 2 \sqrt{5} ( \sqrt{5} x + 4) = 0 \\ \\ = > ( \sqrt{5 } x + 4)(5x + 2 \sqrt{5} ) = 0 \\ \\ = > \sqrt{5} x + 4 = 0 \: \: or \: \: 5x + 2 \sqrt{5} = 0 \\ \\ = > \sqrt{5} x = - 4 \: \: or \: \: 5x = - 2 \sqrt{5} \\ \\ = > x = \frac{ - 4}{ \sqrt{5} } \: \: or \: \: x = \frac{ - 2 \sqrt{5} }{5 } \\ \\ = > x = \frac{ - 4 \times \sqrt{5} }{ \sqrt{5} \times \sqrt{5} } \: \: \: or \: \: x = \frac{ - 2 \sqrt{5} }{5} \\ \\ = > x = \frac{ - 4 \sqrt{5} }{5} \: \: or \: \: x = \frac{ - 2 \sqrt{5} }{5}$

Therefore,

Zeroes are x= -4√5/5 and x= -2√5/5.

Hope it helps ☺️