Question

Find the zeroes of the polynomial p(x)=x2+x-2

Answer 1

≡QUESTION≡

Find the zeroes of the polynomial p(x) = x²+x-2=0

                                                   

║⊕ANSWER⊕║

Given equation,

$x^{2} +x-2=0$

Solving, we get,

$=> x^{2} +2x-x-2=0\\=> x(x+2)-1(x+2)=0\\=>(x-1)(x+2)=0$

Now,

$x-1=0\\=>x=1$

$x+2=0\\=>x=-2$

∴ The zeroes are 1 and -2.

                                                         

Answer 2

x ^{2} + x - 2
= BY THE METHOD OF SPLITTING THE MIDDLE TERM:-
x^{2} +(2 - 1)x - 2
x^{2} + 2x - x - 2
CHANGING THE SIGN:-

x^{2} + 2x - x + 2
x(x + 2) - 1(x + 2)
BY REGROUPING METHOD:-
(x - 1)(x + 2)
p(x) = 0
so,
(x - 1)(x + 2) = p(x)
(x - 1)(x + 2) = 0
so,
(x - 1) = 0 , (x + 2) = 0
(x) = 0 + 1 , (x) = 0 - 2
x = 1 , x = (-2)

SO YOUR ANSWER IS 1 OR (-2).