Question

factorise the polynomial X square + X - 10...what is the answer please solve fast...I will mark u brainliest but no wrong answer please ​

Answer 1

Answer:

(x + $\frac{1}{2}$ + $\frac{\sqrt{41} }{2}$ )(x + $\frac{1}{2}$ - $\frac{\sqrt{41} }{2}$ )

Step-by-step explanation:

solve the polynomial for x then express in product of factor form

Solve

x² + x - 10 = 0 ( add 10 to both sides )

x² + x = 10

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2($\frac{1}{2}$ )x + $\frac{1}{4}$ = 10 + $\frac{1}{4}$

(x + $\frac{1}{2}$ )² = $\frac{41}{4}$ ( take the square root of both sides )

x + $\frac{1}{2}$ = ± $\sqrt{\frac{41}{4} }$ = ± $\frac{\sqrt{41} }{2}$ ( subtract $\frac{1}{2}$ from both sides )

x = - $\frac{1}{2}$ ± $\frac{\sqrt{41} }{2}$

Thus corresponding factors are

(x - (- $\frac{1}{2}$ - $\frac{\sqrt{41} }{2}$ ) ) and (x - (- $\frac{1}{2}$ + $\frac{\sqrt{41} }{2}$ ), that is

(x + $\frac{1}{2}$ + $\frac{\sqrt{41} }{2}$ ) and ( x + $\frac{1}{2}$ - $\frac{\sqrt{41} }{2}$ )

Thus

x² + x - 10 = ( x + $\frac{1}{2}$ + $\frac{\sqrt{41} }{2}$ )(x + $\frac{1}{2}$ - $\frac{\sqrt{41} }{2}$ ) ← in factored form