Question

solve the folowing quadratic equation by factorizition method X^2+X-20=0

Answer 1

Solution:-

Method 1

:- Given equation

=> x² + x - 20

Split into middle term

=> x² + 5x - 4x - 20 =0

=> x( x + 5 ) - 4( x + 5 ) = 0

=> ( x - 4 )(x + 5 ) = 0

=> x - 4 = 0 and x + 5 = 0

=> x = 4 and x = - 5

So value of x is 4 and - 5

Method :- 2

By Quadratic formula

$\boxed{\sf \: \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }$

We have equation

=> x² + x - 20

Compare with :- ax² + bx + c = 0

So

:- a = 1 , b = 1 and c = - 20

put the value on formula

$\sf \: \implies \: x = \dfrac{ - 1 \pm \sqrt{1 {}^{2} - 4 \times 1 \times - 20 } }{2 \times 1}$

$\sf \implies \: x = \dfrac{ - 1 \pm \sqrt{1 + 80} }{2}$

$\sf \implies \: x = \dfrac{ - 1 \pm \sqrt{81} }{2}$

$\sf \implies \: x = \dfrac{ - 1 + 9}{2} \: \: and \: \: x = \dfrac{ - 1 - 9}{2}$

$\rm \implies \: x = \dfrac{8}{2} \: and \: \: x = \dfrac{ - 10}{2}$

$\rm \implies \: x = 4 \: \: and \: \: x = - 5$

Answer 2

Answer:

$\huge {\mathfrak {\orange {given}}}$

${x}^{2} + x - 20 = 0$

$\huge \bf {answer}$

${x}^{2} + 5x - 4x - 20 = 0$

$x(x - 5)-4( x +5) = 0$

$(x - 4) \: (x + 5) = 0$

$x - 4 = 0$

$x + 5 = 0$

$\huge \fbox {x = 4 \: and \: - 5}$