Question

If one zero of the polynomial 2x² + 3x + λ is 1/2, find the value of λ and other zero.​

Answer 1

The value of λ is - 2 and other zero is also - 2.

Justification:

Let p(x) = 2x² + 3x + λ

Its one zero is 1/2, so p(1/2) = 0

p(1/2) = 2 × (1/2)² + 3 × 1/2 × λ

⇒ 1/2 + 3/2 + λ = 0 ⇒ 4/2 + λ = 0

⇒ 2 + λ = 0 ⇒ λ = - 2

Let the other zero be α,

Then α + 1/2 = - 3/2 ⇒α = - 3/2 - 1/2 = - 2

Answer 2

Answer:

Given:– 2x² + 3x + λ

On comparing with ax² + bx + c = 0, we get

• a = 2 b = 3 c = λ

So, plug the value of one zero

• 2 × (1/2)² + 3 × 1/2 + λ = 0
• 1/2 + 3/2 + λ = 0
• 2 + λ = 0
• λ = - 2

Hence, the value of λ for given quadratic equation is -2.