Question

factorise
$6 {x}^{2} - 10x - 76$
​

Answer 1

♦Given:-

p(x)=6x²-10x-76=0

♦To find:-

The value of x?

$\rule{200}{1}$

$\pink{\boxed{\green{\underline{\blue{\mathcal{Proof:-}}}}}}$

→6x²-10x-76=0––divide the equation by 2

→3x²-5x-38=0

★Factorizing using Discriminant method★

•d=b²-4ac

a=3

b=-5

c=-38

★Putting the Values★

→d=(-5)²-4×3×(-38)

→d=25+456

→d=481

→√d=±√481

$\rule{200}{1}$

•Taking x(+)=$\frac{-b+ \sqrt{d}}{2a}$

•x=$\frac{-(5)+ \sqrt{481}}{2×3}$

•x=$\frac{5+ \sqrt{481}}{6}$

$\rule{200}{1}$

•Taking x(-)=$\frac{-b- \sqrt{d}}{2a}$

•x=$\frac{-(5)- \sqrt{481}}{2×3}$

•x=$\frac{5- \sqrt{481}}{6}$

$\rule{200}{5}$

x=$\frac{5± \sqrt{481}}{6}$

Answer 2

Step-by-step explanation:

We Have :-

$6x^{2} - 10x - 76$

To Find :-

$factorise \: it$

Method Used :-

$discriminant \: method$

Solution :-

$6x^{2} - 10x - 76 \\ \\ \\ 3x^{2} - 5x - 38 \\ \\ \\a = 3 \: b = - 5 \: c = - 38 \\ \\ \\ d = b^{2} - 4ac \\ \\ \\ putting \: the \: values \\ \\ \\ d = + - \sqrt{481} \\ \\ \\ now \\ \\ \\ x = \dfrac{ - b - \sqrt{d} }{2a} \\ \\ \\ we \: get \\ \\ \\ x = \dfrac{ - 5 - \sqrt{481} }{6} \\ \\ \\ when \\ \\ \\ x = \dfrac{ - b + \sqrt{d} }{2a} \\ \\ \\ we \: get \\ \\ \\ x = \dfrac{ - 5 + \sqrt{481} }{6}$