Question

Find the zeroes f the following quadratic polynomials and verify the relationship between the zeroes and coefficients.
i) x² - 2x - 8​

Answer 1

Question

Find the zeroes of tge following quadratic polynomials and verify the relationship between the zeroes and coefficient.

(i) x²-2x-8

Answer

x²-2x-8

x²-4x+2x-8

x(x-4)+2(x-4)

(x-4) (x+2)

→ x-4=0

x=4

$\alpha$ =4

→ х+2= 0

х= -2

β= -2

$\alpha$ +β = $\sf{\frac{ - b}{a}}$

4 - 2 = $\sf - {( \frac{ - 2}{ \: \: \: 1} )}$

2=2

$\alpha$ β=$\frac{c}{a}$

4×-2 = $\frac{-8}{1}$

-8=-8

Hence verify.

${\large{\underline{\underline{\sf{\red{Additional \: Information}}}}}}$

Polynomials : An expression$\sf{a_0 + a_1 x + a_2 x² + -- + a_n {x}^{n} \: where \: a_n \: { { \cancel{ = }}}}0$ is called a polynomial in x of degree n.

Quadratic Polynomial : p(x)=ax²+bx+c.