Question

Q10. Given that the roots of the equation 2x^{2}=-2x+3 are a and 3. The equations whose roots are 1/a.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equations whose roots are 1/a, we can use the fact that if r is a root of an equation, then 1/r is a root of the equation formed by replacing x with 1/x.

The given equation is 2x^2 + 2x - 3 = 0.

Let's find the equation whose roots are 1/a by replacing x with 1/x:

2(1/x)^2 + 2(1/x) - 3 = 0

Simplifying the equation:

2/x^2 + 2/x - 3 = 0

Multiplying through by x^2 to eliminate the fractions:

2 + 2x - 3x^2 = 0

This is the equation whose roots are 1/a.