Question

The zeroes of polymomial x2-2x-8 are?

Answer 1

Answer:

refer to the attachment

Answer 2

◇ Question ◇

○ The zeroes of the polynomial $x^{2}-2x-8$are?

$\rule{300}2$

→ on solving given quadratic equation.

$\implies x^{2}-2x-8=0 \\ \implies x^{2}-4x+2x-8=0 \\ \implies x(x-4) +2(x-4)=0 \\\implies (x+2)(x-4) \\ \implies x+2=0,x-4=0 \\ \implies \alpha=-2 \\ \implies \beta = 4$

★ The zeroes of the polynomial

$\implies\alpha+\beta=4+(-2) = 2 \\ \implies \alpha\beta=4(-2)=-8$

$\rule{300}2$

◇ The zeroes of the quadratic polynomial relationship between zeroes and coefficient is.

● Let a is the coefficient of $x^{2},b$ is the coefficient of x and C is constant.

$\implies\alpha+\beta=-\frac{b}{a} \\ \implies \alpha+beta=-\frac{-2}{1} \\ \implies \alpha+\beta=2$

→ verified√√

$\rule{150}3$

$\implies \alpha\beta=\frac{c}{a} \\ \implies \alpha\beta=\frac{-8}{1} \\ \implies \alpha\beta =-8$

→ verified√√

$\rule{300}2$