Question

find all the zeros of the polynomial x^2-2x-8 and verify the relation between its zeros and coffiecent

Answer 1

Answer:-

4 and -2 are the two zeroes of the polynomial X²-2X-8.

Solution :-

P(X) => X²-2X-8

=> X²-4X+2X-8

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

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

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

=> X = 4 OR X = -2

=4 and -2 are the two zeroes of the polynomial X²-2X-8.

RELATIONSHIP BETWEEN THE ZEROES AND COEFFICIENT.

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.

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