Question

14. Find the quadratic polynomial whose zeros are
2/3 and verify the
relation between the coefficients and the zeros of the polynomial.​

Answer 1

Answer:

Here the quadratic equation is x^2-5x+6

Step-by-step explanation:

let's us assume alpha as 2 and beta as 3

alpha +beta =2+3

=5

alpha × beta = 2×3

=6

according the quadratic equation format

x^2 -(alpha + beta )x + (alpha ×beta )

x^2-5x+6

Answer 2

Answer:

x2-5x+6

Step-by-step explanation:

Two Zeroes are- 2 (alpha, a) and 3 (beta, b)

Sum of Zeroes= a+b

=2+3 = 5

Product of Zeroes= ab

= 2×3 = 6

Quadratic Polynomial- x2 - (a+b)x + ab

= x2-5x+6

Verification:- for equation x2-5x+6

Sum of zeroes= a+b = -b/a

2+3 = -(-5)/1

5 = 5

Hence Verified

Product of Zeroes= ab = c/a

2×3 = 6/1

6 = 6

Hence Verified