Question

factories by splitting the middle term x²-22×+117
​

Answer 1

$x^{2} - 22x + 117\\\\x^{2} -13x - 9x +117 \\\\x(x-13)-9(x-13)\\\\(x-13)(x-9 )$

Answer 2

♦Given:-

p(x)=x²-22x+117

♦To Find:-

The Value of x?

$\rule{200}{1}$

♦Proof:-

★Using Discriminant Formula★

→d=b²-4ac

a=1

b=-22

c=117

→d=(-22)²-4×1×117

→d=484-468

→d=16

→√d=±√16

→√d=±4

$\rule{200}{1}$

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

•x→$\frac{-(-22)+4}{2}$

•x→$\frac{\cancel{26}}{\cancel{2}}$

•x=13

$\rule{200}{1}$

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

•x→$\frac{-(-22)-4}{2}$

•x→$\frac{\cancel{18}}{\cancel{2}}$

•x=11

$\rule{200}{1}$

$\boxed{x=9 \ and \ 13}$