Question

4x^2-7x-2=0 solve by factorization​

Answer 1

Step-by-step explanation:

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Answer 2

${{ \text{ \underline {\red{ \underline{Solution}}}}:-}}$

${ \red{ \dashrightarrow{ \mathcal{ \purple{4 {x }^{2} - 7x - 2 = 0 }}}}}$

We take factors of middle term

${ \red{ \dashrightarrow{ \mathcal{ \purple{4 {x }^{2} - 8x + x - 2 = 0 }}}}}$

Take 4x and 1 common from 4x² - 8 and x - 2 respectively.

${ \red{ \dashrightarrow{ \mathcal{ \purple{4x(x - 2) + 1 (x - 2 )= 0 }}}}}$

Collect common terms

${ \red{ \dashrightarrow{ \mathcal{ \purple{4x(x - 2) + 1 (x - 2 )= 0 }}}}}$

${ \red{ \dashrightarrow{ \mathcal{ \purple{(4x + 1)(x - 2) = 0 }}}}}$

Now,

${ \red{ \dashrightarrow{ \mathcal{ \purple{4x + 1 = 0 \: \: \: \: \: \: or \: \: \: \: \: \: \: x - 2 = 0 }}}}}$

${ \red{ \dashrightarrow{ \mathcal{ \purple{x = - \frac{1}{4} \: \: \: \: \: \: or \: \: \: \: \: \: \: x = 2 }}}}}$

Hence, the roots of above equation is - 1/4 & 2 .