Question

Find the zeroes of the polynomial x2 +-X-2 and verify the relationship between the coefficient
and zeroes of the polynomial.​

Answer 1

Answer:

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x=2 or x= -1

Step-by-step explanation:

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

Splitting the middle term

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

x+1=0            or.           x-2=0

x= -1.                             x=2

VERIFICATION

we know that

$\alpha+\beta =\frac{-b}{a}$

also

$\alpha \beta=\frac{c}{a}$

here

a= 1,    b= -1,   c=-2

$\alpha+\beta =\frac{-b}{a}$

-1 + 2 = $\frac{-(-1)}{1}$

1=1

now,

$\alpha \beta=\frac{c}{a}$

2*(-1)= $\frac{-2}{1}$

-2 = -2

Hence verified