Question

1. Find a quadratic polynomial whose zeroes are I and -3. Verify the relation between
the coefficient and zeroes of the polynomial.​

Answer 1

Answer:

let the alpha be 1and beta be -3

sum of zeoes =alpha +beta

1+-3=-2

product of zeroes =alpha×beta

1×-3=-3

required polynomial=x^2-(sum of zeroes)x+product of zeroes

x^2-2x+3

Answer 2

ANSWER

Let f(x)=2x ^2 −7x

In this the constant term is zero. f(x)=2x ^2−7x

=x(2x−7)

x(2x−7)=0⇒2x−7=0 or x=0

2−7x=x(2x−7)On putting f(x)=0, we get x(2x−7)=0⇒2x−7=0 or x=0⇒x= 7/2

or x=0

Thus, the zeroes of the given polynomial 2x ^2−7x are 0 and 7/2

Verification :Sum of zeroes =α+β=0+ 7/2= 7/2

Coefficient of x = − (−7)/2

=7/2

Product of zeroes =αβ=0× 7/2

Constant term

______________

Coefficient of x

=0/2

=0

So, the relationship between the zeroes and the coefficients is verified.