Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their confficient .x2-2x-8​

Answer 1

Answer:

4 and -2 are the two zeroes of the polynomial X²-2X-8. ... Sum of zeroes = Alpha + Beta = 4 + (-2) = 4-2 = 2/1 = Coefficient of X/Coefficient of X². And, Product of zeroes = Alpha × Beta = 4 × -2 = -8/1 = Constant term/Coefficient of X².

Answer 2

Answer:

${x}^{2} - 2x - 8 = {x}^{2} - 4x + 2x - 8 \\ 0 = x(x - 4) + 2(x - 4) \\ 0 = (x - 4)(x + 2)$

(x-4)=0

x=4

(x+2)=0

x=-2

Therefore, the zeroes of the given polynomial are 4 and -2.

$sum \: of \: zeroes = \alpha + \beta \\ = 4 + ( - 2) = 2 \\ \frac{ - b}{a} = \frac{ - ( - 2)}{1} = 2 \\ therefore \: \alpha + \beta = \frac{ - b}{a} \\ product \: of \: zeroes = \alpha \beta \\ = 4( - 2) = - 8 \\ \frac{c}{a} = \frac{ - 8}{1 } = - 8 \\ therefore \: \alpha \beta = \frac{c}{a}$