Question

solve the equation by factorisation 4 root 5x2 +3x - 2 root 5​

Answer 1

Answer:

5x2 + 3x-2

5x2+5x-2x-2

5x(2) -2(x)

5x-2 as 2/5 & 1/2 are the roots .

hope its help u mark it as a brainlist answer

Answer 2

Answer :-

$\implies \boxed{ \frac{ - 2}{ \sqrt{5} } , \frac{ \sqrt{5} }{4} }$

To Find :-

→ Factors of the given quadratic equation .

Explanation :-

Given quadratic is -

$\to \sf{ 4 \sqrt{5} {x}^{2} + 3x - 2 \sqrt{5} = 0}$

Split the middle term .

$\to \sf{4 \sqrt{5} {x}^{2} + (8 - 5)x - 2 \sqrt{5} = 0} \\ \\ \to \sf{4 \sqrt{5} {x}^{2} + 8x - 5x - 2 \sqrt{5} = 0} \\ \\ \to \sf{ 4x( \sqrt{5} x + 2) - \sqrt{5} ( \sqrt{5} x + 2) = 0} \\ \\ \sf{ \to( \sqrt{5} x + 2)(4x - \sqrt{5} ) = 0} \\ \\ \star \: \: \bf{ \underline{ case }\: (1)} \\ \\ \leadsto \sf{ \sqrt{5} x + 2 = 0 }\\ \\ \leadsto \sf{ \sqrt{5} x = - 2}$

$\leadsto \boxed{ \sf{x = - \frac{2}{ \sqrt{5} } }} \\ \\ \star \: \bf{\underline{ case }\: (2)} \\ \\ \leadsto \sf{ 4x - \sqrt{5} = 0} \\ \\ \leadsto \boxed{\sf{ x = \frac{ \sqrt{5} }{4} }}$

Verification :-

Replace these values in given quadratic

$(1) \to \: 4 \sqrt{5} {( \frac{ - 2}{ \sqrt{5} }) }^{2} + 3 \times \frac{( - 2)}{ \sqrt{5} } - 2 \sqrt{5} = 0 \\ \\ \to \: \frac{16}{ \sqrt{5} } - \frac{6}{ \sqrt{5} } - 2 \sqrt{5} = 0 \\ \\ \to \: \frac{16 - 6 - 10}{ \sqrt{5} } = 0 \\ \\ \to \boxed{ 0 = 0 }\\ \\ (2) \to \: 4 \sqrt{5} \times \frac{ {5} }{16} + 3 \times \frac{ \sqrt{5} }{4} - 2 \sqrt{5} = 0 \\ \\ \to \: \frac{5 \sqrt{5} }{4} + \frac{3 \sqrt{5} }{4} - 2 \sqrt{5} = 0 \\ \\ \to \: \frac{8 \sqrt{5} - 8 \sqrt{5} }{4} = 0 \\ \\ \to \: 0 = 0$

hence verified