Question

11. Find the Quadratic Polynomial the sum and product of whose Zeroes are -3 and 2
respectively​

Answer 1

Given :-

Sum of zeroes of a quadratic polynomial = -3

And product of it's zeroes = 2

We know that,

Sum of zeroes = -b/a

Product of zeroes = c/a

Therefore,

-b/a = -3

➡ b/a = 3

➡ b = 3 and a = 1

Similarly,

c/a = 2

➡ c = 2 and a = 1

Since a = 1 in both place. We don't need to take LCM.

➡ a = 1, b = 3 and c = 2

Standard form of a quadratic polynomial/equation = ax² + bx + c = 0

Hence, the quadratic polynomial is x² + 3x + 2

Answer 2

Answer :-

The Quadratic polynomial is x² + 3x + 2.

Solution :-

Given

Sum of zeroes = α + β = - 3

Product of zeroes = αβ = 2

Quadratic polynomial ax² + bx + c = k{x² - x(α + β) + αβ}

(where k ≠ 0)

By substitutong the given values

= k{x² - x(-3) + 2}

= k(x² + 3x + 2)

When k = 1

= 1(x² + 3x + 2)

= x² + 3x + 2

Therefore the Quadratic polynomial is x² + 3x + 2.