Question

If sum of the zeroes of ky2+2y is equal to twice their product then k is?

Answer 1

Your Question is incomplete mate.

Question :

If sum of the zeroes of ky² +2y - 3k is equal to twice their product then k is?

Solution:

We have f(x) = ky² + 2y - 3k

On comparing with ax² + bx + c, we get

a = k, b = 2, c = -3k

Let α,β be the zeroes of f(x).

Sum of zeroes(α + β) = -b/2a

=> α + β = -2/k

Product of zeroes = c/a

=> αβ = -3k/k

=> αβ = -3

It is said that Sum of zeroes is equal to twice their product.

∴ α + β = 2αβ

=> -2/k = 2(-3)

=> 2/k = 6

=> 2 = 6k

=> k = 1/3

Hence, the value of k = 1/3.

#BeBrainly

Answer 2

Solution:

We have f(x) = ky² + 2y - 3k

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3k

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3kLet α,β be the zeroes of f(x).

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3kLet α,β be the zeroes of f(x).Sum of zeroes(α + β) = -b/2a

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3kLet α,β be the zeroes of f(x).Sum of zeroes(α + β) = -b/2a=> α + β = -2/k

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3kLet α,β be the zeroes of f(x).Sum of zeroes(α + β) = -b/2a=> α + β = -2/kProduct of zeroes = c/a

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3kLet α,β be the zeroes of f(x).Sum of zeroes(α + β) = -b/2a=> α + β = -2/kProduct of zeroes = c/a=> αβ = -3k/k

We have f(x) = ky² + 2y - 3kOn comparing with ax² + bx + c, we get a = k, b = 2, c = -3kLet α,β be the zeroes of f(x).Sum of zeroes(α + β) = -b/2a=> α + β = -2/kProduct of zeroes = c/a=> αβ = -3k/k=> αβ = -3

∴ α + β = 2αβ

∴ α + β = 2αβ=> -2/k = 2(-3)

∴ α + β = 2αβ=> -2/k = 2(-3)=> 2/k = 6

∴ α + β = 2αβ=> -2/k = 2(-3)=> 2/k = 6=> 2 = 6k

∴ α + β = 2αβ=> -2/k = 2(-3)=> 2/k = 6=> 2 = 6k=> k = 1/3

∴ α + β = 2αβ=> -2/k = 2(-3)=> 2/k = 6=> 2 = 6k=> k = 1/3Hence, the value of k = 1/3.