Question

8) Form a quadratic polynomial p(x) with 3 and -2/5 as sum and product of its zeroes , respectively.

Answer 1

Given,

• Zeroes of quadratic polynomial is 3 and -2/5 respectively.

To Find,

• Quadratic polynomial.

According to question,

★ Sum of zeroes,

⇒ α + β

⇒ 3 + (-2/5)

⇒ 3 - 2/5

⇒ 15-2/5

⇒ 13/5

★ Product of zeroes,

⇒ αβ

⇒ 3 × (-2/5)

⇒ -6/5

We know that,

Quadratic polynomial,

⇒ x² - (α + β)x + αβ

[ Put the values ]

⇒ x² - (13/5)x + (-6/5)

⇒ x² - 13/5 x - 6/5

Therefore,

The quadratic polynomial is x² - 13/5 x - 6/5.