Question 76

If one root of the equation $$(1— m)x^2 + 1 = 0$$ is double the other and 'I' is a real number, then which of the following 6 is true?

Solution

$$(l— m)x^2 + 1 = 0$$

Let a and 2a be the roots of the equation

Sum of roots

$$a+2a = \frac{-l}{l-m}$$

$$a = \frac{-l}{3(l-m)}$$ ---1

Product of roots

$$a\times 2a = 2a^2 = \frac{1}{l-m}$$ ---2

putting 1 in 2

$$\frac{2l^2}{9(l-m)^2} = \frac{1}{l-m}$$

$$2l^2 = 9(l-m)$$

$$2l^2-9l+9m = 0$$

As l is a real number, Discriminant > 0

$$81 - 72m \geq 0$$

$$9-8m \geq 0$$

$$m \leq \frac{9}{8}$$

Option D is correct.

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