Question

b.Thevalueofkforwhichtherootsoftheequation2x

2+kx+k–3=0arereciprocaltoeach other is​

Answer 1

Question :

The value of k for which the roots of the equation 2x² + kx + k - 3 = 0 are reciprocal to eachother is :

Solution :

According to the Question,

If ∅ is one root of the given equation, then 1/∅ would be the other root.

We know that,

Product of roots = Constant Term/x² coefficient

Thus,

$\longrightarrow$ ∅ × 1/∅ = (k - 3)/2

$\longrightarrow$ 1 = (k - 3)/2

$\longrightarrow$ 2 = k - 3

$\longrightarrow$ k = 5.

For k = 5, roots of the above equation would be reciprocal to eachother.

When k = 5, the equation would become 2x² + 5x + 2 = 0.

Verification :

2x² + 5x + 2

$\longrightarrow$ 2x² + 4x + x + 2

$\longrightarrow$ 2x(x + 2) + 1(x + 2)

$\longrightarrow$ (2x + 1)(x + 2)

Using Factor Theorem,

2x + 1 = 0 or, x + 2 = 0

Thus, x = -2 or -1/2.

Henceforth, Proved.