Question

Form a quadratic polynomial whose sum and product of the zeroes are 2 and -3/5 respectively.

Answer 1

Answer:

x^2-(a+b)x+ab,

x^2-2x-(3/5),

5x^2-10x-3.

Answer 2

The required quadratic equation is 5x²+10x+3 = 0.

Given:

The sum and product of the zeroes of a quadratic polynomial are 2 and -3/5 respectively.

To Find:

The required quadratic polynomial.

Solution:

A quadratic polynomial is a polynomial having degree 2. Its general form is ax²+bx+c = 0, where a, b, and c are integers and a≠0.

In a quadratic polynomial

Sum of zeros = -b/a  

Product of zeros = c/a

If we divide the entire polynomial ax²+bx+c = 0 by -a, we get:

x² + (-b\a)x - (c\a) = 0

⇒ The quadratic polynomial = x² + (Sum of zeros)x - (Product of zeros).

We have been given that

The sum of zeros = 2

The product of zeros = -3/5

Hence, the quadratic equation becomes,

x²+2x-(-3/5) = 0

⇒ 5x²+10x+3 = 0.

∴ The required quadratic equation is 5x²+10x+3 = 0.

#SPJ2