Question

if 2 is the one root of the equation kx2+2x-3=0 then find the value of K
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Answer 1

Answer:

The required value of k is -1/4

Step-by-step explanation:

Given :

2 is one root of the equation kx² + 2x - 3 = 0

To find :

the value of k

Solution :

Let p(x) = kx² + 2x - 3

As 2 is a root of the given equation, when we substitute x = 2 the result is zero.

i.e., p(2) = 0

Put x = 2,

k(2)² + 2(2) - 3 = 0

 4k + 4 - 3 = 0

 4k + 1 = 0

  4k = -1

   k = -1/4

Therefore, the value of k is -1/4

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Verification :

Put k = -1/4 and x = 2,

 kx² + 2x - 3 = 0

(-1/4)(2)² + 2(2) - 3 = 0

 (-1/4)(4) + 4 - 3 = 0

  -1 + 1 = 0

  0 = 0

 LHS = RHS

Hence verified!

Answer 2

x = 2 is the root of the equation kx² + 2x - 3 = 0.

Putting x = 3 in the given equation,

we get

k(2)² + 2(2) - 3 = 0

4k + 4 - 3 = 0

4k + 1 = 0

4k = -1

k = -1/4

Hence, the value of k is -1/4.