Question

find the other zeroes of the following polynomial 5√5x2+30x+8√5

Answer 1

$\Longrightarrow{\boxed{\bold{Answer: See\:below}}}$

$\textbf{\underline{Step-by-step explanation :- }}$

$\bold{5 \sqrt{5} {x}^{2} + 30x + 8 \sqrt {5} = 0} \\ \\ \bold{5 \sqrt{5} {x}^{2} + 20x + 10x + 8 \sqrt{5} = 0} \\ \\ \bold{ 5x( \sqrt{5} x + 4) + 2 \sqrt{5} ( \sqrt{5} x + 4) = 0} \\ \\ \bold{\underline{Taking \: \sqrt{5} x + 4 \: as \: common}} \\ \\ \bold{(5x + 2 \sqrt{5} )( \sqrt{5} x + 4) = 0} \\ \\ \bold{\underline{Each \: getting \: zero}} \\ \\ \bold{5x + 2 \sqrt{5} = 0} \\ \bold{5x = - 2 \sqrt{5} = > x = \frac{ - 2 \sqrt{5} }{5}} \\ \\ \bold{Similarly \: \sqrt{5} x + 4 = 0} \\ \bold{ \sqrt{5} x = - 4 = > x = \frac{ - 4}{ \sqrt{5} } } \\ \\ \bold{\underline{On\:rationalizing\:we\:get}} \\ \\ \bold{x = \frac{ - 4}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{ - 4 \sqrt{5} }{5} } \\ \\ \bold{So \: zeros\:are\: \frac{ - 2 \sqrt{5} }{5} \: and \: \frac{ - 4 \sqrt{5} }{5} }$

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 )