Question

factorize


x²- 22x+117​

Answer 1

Answer:

Step-by-step explanation:

Given :-

x² - 22x + 117

To Factorize :-

x²- 22x + 117​

Solution :-

Now, first we have to find out two numbers p and q

Such that p + q = -22 and pq = 117

So clearly,

13 + 9 = -22 and 13 × 9 = 117

So, numbers are 13 and 9,

Now, split the middle term of 22x

 = x² - 22x + 117

= x² - 13x - 9x + 117

 = x(x - 13) - 9(x - 13)

= (x - 13)(x - 9)

Hence, Required Data is  (x - 13)(x - 9) .

Answer 2

$\sf \large \red{ \underline{ \underline{ \: Given : \: \: \: }}}$

$\star$ x² - 22x + 117 = 0

$\sf \large \red{ \underline{ \underline{ \: To \: find : \: \: \: }}}$

$\star$ Roots of the quadratic equation

$\sf \large \red{ \underline{ \underline{ \: Solution : \: \: \: }}}$

By middle term splitting method ,

$\sf \implies {x}^{2} - 22x + 117 = 0 \\ \\ \sf \implies {x}^{2} - 13x - 9x + 117 = 0 \\ \\ \sf \implies x(x - 13) - 9(x - 13) = 0 \\ \\ \sf \implies (x - 9)(x - 13) = 0 \\ \\ \sf \implies x = 9 \: , \: x = 13$

Therefore , the roots are 9 and 13