Question

Find a quadratic polynomial,the sum and product of whose zeroes are -3 and 2 respectively.hence find the zero

Answer 1

sum of the zeoes = -3
product of the zeroes = 2

p(x) = x² - (sum of zeroes)x + product of zeores
= x² -(-3)x + 2
= x² +3x +2

for the zeroes:-
x² +(2+1)x +2
x²+2x + x + 2
x(x+2) +1(x+2)
(x+1) (x+2)

thus the zeroes are -1 & -2

hope this helps

Answer 2

Sum of zeros ( alpha + beta) = -3

Product of zeros ( alpha × beta) = 2.

Quadratic polynomial = X²-(alpha + beta)X+ Alpha× beta = X²-(-3)X+2.

= X²+3X+2 is required quadratic polynomial.

A = 1 , b = 3 , C = 2

X²+ 3 X +2

X² + 2X+ X + 2

X(X+2) +1 ( X+2)

(X+2). ( X+1)

X+2 = 0. X+1 = 0

X = -2. X= -1

ZEROS OF THE QUADRATIC POLYNOMIAL X²+3X+2 are -2 and -1.

HOPE IT WILL HELP YOU.
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