Question

zoros
polyesos
of the quadratic
the relatsonship
grous and the cofficents
and verify
x²-2x-8​

Answer 1

Step-by-step explanation:

f(x) = 2 − 2 − 8

() = 2 − 2 − 8

= 2 − 4 + 2 − 8

= ( − 4) + 2( − 4)

= ( + 2)( − 4)

Zeroes of the polynomials are -2 and 4

Sum of the zeroes

-coefficient of x

coefficient of x

=-coefficient of xcoefficient of x

-2+4=-(-2)1

2 = 2

Product of the zeroes

constant term

coefficient of

=constant termcoefficient of x2

-2×4=-81

-8=-8

SOLUTION 2

x2 - 2x- 8 = x2 - 4x + 2x - 8

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

= (x - 4)(x + 2)

Therefore the zeroes of the polynomial x2 - 2x - 8 are {4, 2}

Relationship between the zeroes and the coefficients of the polynomial

Sum of the zeroes = - (

Also sum of the zeroes of the polynomial = 4 - 2 = 2

Product of the zeroes = (

Also product of the zeroes = 4 x -2 = -8

Hence verified

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