Question

x*2-3x-10=0 ko sutra vidhi se hal kijiye ​

Answer 1

Solution:-

Method :-1 using factorization method

$\rm \implies {x}^{2} - 3x - 10 = 0$

Split into middle term

$\rm \implies {x}^{2} - 5x + 2x - 10 = 0$

$\implies \rm x(x - 5) + 2(x - 5) = 0$

$\rm \implies(x + 2)(x - 5) = 0$

$\rm\implies \: x + 2 = 0 \: and \: x - 5 = 0$

$\rm \implies \: x = - 2 \: \: and \: \: x = 5$

Method:- 2 using quadratic formula

$\rm \implies {x}^{2} - 3x - 10 = 0$

Compare with

$\rm \implies \: a {x}^{2} + bx + c = 0$

So

$\rm \implies \: a = 1 ,\: b = - 3 \: and \: c = - 10$

Quadratic formula

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

Put the value

$\rm \implies \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) ^{2} - 4 \times 1 \times - 10} }{2 \times 1}$

$\rm \implies \: x = \dfrac{3 \pm \sqrt{9 + 40} }{2}$

$\rm \implies \: x = \dfrac{3 \pm \sqrt{49} }{2}$

$\rm \implies \: x = \dfrac{3 + 7}{2} \: and \: x = \dfrac{3 - 7}{2}$

$\implies \rm \: x = \dfrac{10}{2} \: and \: x = \dfrac{ - 4}{2}$

$\rm \implies \: x = 5 \: \: and \: x = - 2$

Answer 2

$\huge\bf\underline\purple{Solution}$

Step by step explanation:-

Given Q.E x²-3x-10=0

Finding factors:-

1× -10

2× -5

5× -2

Their sum should be -3 So,If u take -5,2 Sum is -3 So,factors are -5x +2x

Split the middle term

x² -3x -10 =0

x² -5x +2x - 10 = 0

Take the common in 4 terms

x(x - 5) +2 (x -5)

(x -5)(x+ 2) hence factorised

So, x²-3x+10 = (x-5)(x+2)

Finding roots:-

x - 5 = 0

x = 5

x + 2 = 0

x = -2

So, roots of given Quadratic equation is 5,-2