Question

Find a quadratic polynomial, the sum and product of whose zeros are -1/3 and 4.

Answer 1

Given :-

• Sum of zeroes = -1/3
• Product of zeroes = 4

To find :-

Quadratic polynomial = ?

Solution :-

When we know the sum and product of zeroes and when we are supposed to find the quadratic polynomial, we use the below mentioned formula.

Quadratic polynomial = x² - (α + β)x + αβ

Where

• (α + β) is the sum of zeroes
• αβ is the product of zeroes

Quadratic polynomial = x² - (α + β)x + αβ

➝ Quadratic polynomial = x² - (-1/3)x + 4

⇒ Quadratic polynomial = x² + 1/3x + 4

Here we Multiply 3 throughout the polynomial to eleminate the fraction.

➥ Quadratic polynomial = 3x² + x + 12

KNOW MORE:

α and β are the general zeroes of all polynomials because when the given equation is factorised, the factors are got. When these factors are equated to zero we get the value of α and β.