Question

Find the zeroes of the polynomial x^2-4 and verify the relationship between the zeroes and coefficients.also for6x^2+7x+2.

Answer 1

Hii friend,

P(X) = X²-4

=> X²-(2)² = (X+2) (X-2)

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

=> X = -2 OR X = 2

-2 and 2 are the two zeros of the polynomial X²-4.

Let Alpha = -2 and Beta = 2

Relationship between the zeros and the coefficient.

Sum of zeros = (Alpha + Beta) = (-2 + 2) = 0/1 = Coefficient of X/Coefficient of X².


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

(2) 6X²+7X+2

=> 6X²+3X+4X+2

=> 3X(2X+1) +2(2X+1)

=> (2X+1) (3X+2)

=> (2X+1) = 0 OR (3X+2) = 0

=> X = -1/2 OR X = -2/3

-1/2 and -2/3 are the two zeros of the polynomial 6X²+7X+2

Let Alpha = -1/2 and Beta = -2/3

Sum of zeros = (Alpha + Beta) = (-1/2 + (-2/3} = -1/2 -2/3 = -3-4/6 = -7/6 = -(Coefficient of X/Coefficient of X²)

Product of zeros = (Alpha × Beta) = (-1/2 × -2/3) = 2/6= Constant term/Coefficient of X²

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