Question

$3 {x}^{2} + 12x - 288 = 0$
Solve​

Answer 1

ANSWER :

We can solve the question 2 methods

Method 1 : Using quadratic equation formula

Method 2 : Using factorisation

Quadratic equation

3x² + 12x - 288 = 0

METHOD 1 :

Using quadratic equation formula

${ \bf \red{ \to x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}$

Here ,

In the given quadratic equation divide with 3 on both sides

We get

x² + 4x - 96 = 0

a = 1 , b = 4 , c = - 96

Substitute

${ \sf{ \to x = \frac{ - 4 \pm \sqrt{( {4})^{2} - 4(1)( - 96)} }{2(1)} }}$

${ \sf{ \to x = \frac{ - 4 \pm \sqrt{16 + 384} }{2} }}$

$\to{ \sf{x = \frac{ - 4 \pm \sqrt{400} }{2} }}$

$\to{ \sf{x = \frac{ - 4 + 20}{2}(or) \frac{ - 4 - 20}{2} }}$

$\to{ \sf{x = 8(or) - 12}}$

Hence x = 8 (or) -12

METHOD 2 :

3x² + 12x - 288 = 0

Divide with 3 on both sides

We get

x² + 4x - 288 = 0

Split the middle term

x² + 12x - 8x - 288 = 0

Taking common

x(x + 12) - 8(x + 12) = 0

(x + 12)(x - 8) = 0

x = -12 (or) 8