Question

find the zeros of the polynomial quadratic polynomial and verify the relationship between the zeros and the coefficients x square - 2 x minus 8

Answer 1

x^2 - 2x - 8

=> x^2 - 4x + 2x - 8

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

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

Zeroes are 4 and (-2)

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Verification :-

Sum of zeroes = - b / a

=> 4 + (-2) = - ( - 2) / 1

=> 4 - 2 = 2

=> 2 = 2

LHS = RHS


Product of zeroes = c/a

=> ( 4)(-2) = - 8 / 1

=> - 8 = - 8

LHS = RHS

Answer 2

Hii friend,

P(X) = X²-2X-8


=> X²-4X+2X-8

=> X(X-4)+2(X-4)

=> (X-4)(X+2)

=> (X-4) = 0 OR (X+2) = 0

=> X = 4 OR X = -2

Two zeros of the polynomial X²-2X-8 = 4 and-2

Let Alpha = 4 and Beta = -2

Therefore,

Sum of zeros = (Alpha + Beta) = (4+(-2) = 2/1 = Coefficient of X / Coefficient of X².

Product of zeros = (Alpha × Beta) = (4×(-2) = -8/1 = Constant term/ Coefficient of X².


HOPE IT WILL HELP YOU.... :-)