Question

$\begin{gathered}\boxed{\begin{array}{|c| c|}\cline{1-2}\bf{Discriminant}&\bf{Nature}\\\cline{1-2}\sf{-ve}&\sf{No\:real\:roots}\\\cline{1-2} \sf{+ve}&\sf{Two\:distinct\:roots}\\\cline{1-2}\sf{0}&\sf{Two\:equal\:roots}\\\cline{1-2}\end{array}}\end{gathered}$

$\rule{300}{2}$

Solve the following quadratic equation by formula method.

$\bull$x²+2x–5=0. ​

​

Answer 1

Answer:

$x = 2 + \sqrt{6} \: or \: x = 2 - \sqrt{6}$

Step-by-step explanation:

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

$comparing \: with \: a{x}^{2} + bx + c = 0 \: \: \: we \: get$

a = 1, b = 2,c = -5

${b}^{2} - 4ac = {(2)}^{2} - 4 \times 1 \times ( - 5)$

$= 4 - ( - 20)$

$= 4 + 20$

$= 24$

$x = \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} - 4ac} }{2a}$

$= \frac{ - {2}^{2} \binom{ + }{ - } \sqrt{24} }{2 \times 1}$

$= \frac{4 \binom{ + }{ - } 2 \sqrt{6} }{2}$

$= \frac{2(2 \binom{ + }{ - } \sqrt{6} ) }{2}$

$x = 2 \binom{ + }{ - } \sqrt{6}$

$x = 2 + \sqrt{6} \: or \: x = 2 - \sqrt{6}$

Answer 2

Answer:

tion:

{x}^{2} + 2x - 5 = 0x2+2x−5=0

comparing \: with \: a{x}^{2} + bx + c = 0 \: \: \: we \: getcomparingwithax2+bx+c=0weget

a = 1, b = 2,c = -5

{b}^{2} - 4ac = {(2)}^{2} - 4 \times 1 \times ( - 5)b2−4ac=(2)2−4×1×(−5)

= 4 - ( - 20)=4−(−20)

= 4 + 20=4+20

= 24=24

x = \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} - 4ac} }{2a}x=2a−b(−+)b2−4ac

= \frac{ - {2}^{2} \binom{ + }{ - } \sqrt{24} }{2 \times 1}=2×1−22(−+)24

= \frac{4 \binom{ + }{ - } 2 \sqrt{6} }{2}=24(−+)26

= \frac{2(2 \binom{ + }{ - } \sqrt{6} ) }{2}=22(2(−+)6)

x = 2 \binom{ + }{ - } \sqrt{6}x=2(−+)6

x = 2 + \sqrt{6} \: or \: x = 2 - \sqrt{6}x=2+6orx=2−6