Question

find the root of equation x^2 +5x -6 =0​

Answer 1

Step-by-step explanation:

x^2 + 5x = 6

$\sqrt{x ^{2} + 5x }$

$x \sqrt{5x}$

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Answer 2

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★ Find the roots of the Equation =>

x² + 5x - 6 = 0

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We can find the roots of this Equation using two methods .

★ First Method :

# Splitting the middle term .

$\mapsto \rm \: {x}^{2} + 5x - 6 = 0$

$\mapsto \rm \: {x}^{2} + 6x - x - 6 = 0$

$\mapsto \rm \: x(x + 6) - 1(x + 6) = 0$

$\mapsto \rm \: (x - 1)(x + 6) = 0$

So ,

Either,

$\rightarrow \rm \: (x - 1) = 0 \\ \implies \boxed{ \rm \: \: x = 1 \: }$

Or,

$\rightarrow \rm \: (x + 6) = 0 \\ \implies \boxed{ \rm \: x = - 6 \: }$

$\star\boxed{ \sf{roots = (1) \: and \: (- 6)}}$

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★ Second Method :

# Using Quadratic Formula.

$\boxed{ \rm \: {x}^{2} + 5x - 6 = 0}$

Here ,

• a = 1
• b = 5
• c = -6

So ,

$\rm \mapsto \: roots \: = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a}$

$\mapsto \rm \: roots \: = \dfrac{ - 5 \pm \: \sqrt{ {(5)}^{2} - 4 \times 1 \times ( - 6)} }{2 \times 1}$

$\mapsto \rm \: roots \: = \dfrac{ - 5 \pm \: \sqrt{25 + 24} }{2}$

$\mapsto \rm \: roots \: = \dfrac{ - 5 \pm \sqrt{49} }{2}$

$\mapsto \rm \: roots \: = \dfrac{ - 5 \pm \: 7}{2}$

So ,

$\rm \: first \: root \: = \dfrac{ - 5 + 7}{2}$

$\implies \boxed{ \rm \: first \: root \: = \frac{ \cancel2}{ \cancel2} = 1}$

and ,

$\rm \: second \: root \: = \: \dfrac{ - 5 - 7}{2}$

$\implies \boxed{ \rm \: second \: root \: = \frac{ - \cancel{12}}{ \cancel2} = - 6 }$

So ,

$\star \boxed{ \sf \: roots \: are \: (1) \: and \: ( - 6)}$