Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

From the equation, we can rewrite it as:

2x^2 + 2x - 3 = 0

Now, we can use Vietas formulas to relate the roots of the quadratic equation to the coefficients of the quadratic equation.

The sum of the roots, a + 3 = -2/2 = -1
The product of the roots, a * 3 = -3/2

Now we need to find the expressions for 1/a and 1/b.

Let 1/a = m and 1/3 = n.

From Vietas formulas, we know that the sum and product of roots remain the same if we take the reciprocal of the roots. Therefore, we can use the same formulas to find the relationship between m and n.

The sum of the reciprocals of the roots, m + n = -1
The product of the reciprocals of the roots, mn = -3/2

Thus, the equations whose roots are 1/a and 1/b are:

m + n = -1
mn = -3/2