factories by splitting the middle term x²-22×+117
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[tex]x^{2} - 22x + 117\\\\x^{2} -13x - 9x +117 \\\\x(x-13)-9(x-13)\\\\(x-13)(x-9 )\\[/tex]
♦Given:-
p(x)=x²-22x+117
♦To Find:-
The Value of x?
[tex]\rule{200}{1}[/tex]
♦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
[tex]\rule{200}{1}[/tex]
•Taking x(+)=[tex] \frac{-b+ \sqrt{d}}{2a} [/tex]
•x→[tex] \frac{-(-22)+4}{2} [/tex]
•x→[tex] \frac{\cancel{26}}{\cancel{2}} [/tex]
•x=13
[tex]\rule{200}{1}[/tex]
Taking x(-)=[tex] \frac{-b- \sqrt{d}}{2a} [/tex]
•x→[tex] \frac{-(-22)-4}{2} [/tex]
•x→[tex] \frac{\cancel{18}}{\cancel{2}} [/tex]
•x=11
[tex]\rule{200}{1}[/tex]
[tex]\boxed{x=9 \ and \ 13} [/tex]