Question

solve 2x² + 9x- 56 = 0 using quadratic formula and also find nature of the roots​

Answer 1

$\huge\mathbb\red{ANSWER}$

by using quadratic formula

$\huge\color{brown}\boxed{x=\frac{-b±\sqrt{{b}^{2} - 4ac }}{2a}}$

where a = 2, b= 9 and c = -56

$x = \frac{ - 9 ± \sqrt{ {9}^{2} - 4(2)( - 56) } }{2(2)} \\ \\ x = \frac{ - 9± \sqrt{81 + 448 } }{4} \\ \\ x = \frac{ - 9 ± \sqrt{529} }{4}$

from there two cases

$case \: {1}^{st} \\ \\ x = \frac{ - 9 + 23}{4} \\ \\ x = \frac{14}{4} = 3.5 - - -( 1 \: value)$

$case \: {2}^{nd} \\ \\ x = \frac{ - 9 - 23}{4} \\ \\ x = \frac{ - 32}{4} = 8 - - - (2nd \: value)$

Now nature of roots

$\huge \color{yellow} \boxed{d = {b}^{2} - 4ac}$

by putting value

$d = { - 9}^{2} - 4(2) (- 56) \\ \\ d = 81 + 448 \\ \\ d = 529$

$clearly \: d > 0 \: \: so \: roots \: are \: real \: and \: unequal \:$

$\huge\mathbb\green{EXPALNATION}$

• we use quratic fromula to find roots first

• as we know at last of of we have two conditions or say two value

• a quadratic equations has allways two value

• then we find nature of roots by using d

• is d = 0 then roots are real and equal

• if it is d < 0 then roots are imaginary and unequal

• it is d > 0 then root is real and distinct or say unequal

$\huge\mathbb\blue{EXTRAINFO}$

quadratic equations. :- an equation which has highest power as 2

quadratic formula:- formula which is use to obtain value of quadratic equation also know as shridhar achrya formula

hope it helps you

be brainly