Question

For what values of $x,$ the numbers $-1,x,$ $-\frac{3}{4}$ are in GP?

• A. $\frac{3}{2}$
• B. $\sqrt{\frac{3}{4}}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\frac{3}{\sqrt{2}}$

Answer 1

The correct option is B

$\sqrt{\frac{3}{4}}$

Explanation for the correct options:

Given Data:

$-1,x,$ $-\frac{3}{4}$ are in GP

$$\begin{gathered} weknowthat \\ ifa,bandcareinG.P.,Thenwehave \\ {b}^2=ac \end{gathered}$$

$\Rightarrow x^2=(-1)(-\frac{3}{4})$

$\Rightarrow x=\sqrt{\frac{3}{4}}$

Hence, Option(B) is correct