If α and β are roots of the equation x2−3x+a=0 and γ and δ are roots of the  equation x2−12x+b=0 and α,β,γ,δ form an increasing  GP, then the values  of a and b are respectively

# If $\mathrm{\alpha }$ and $\mathrm{\beta }$ are roots of the equation ${\mathrm{x}}^{2}-3\mathrm{x}+\mathrm{a}=0$ and $\gamma$ and $\mathrm{\delta }$ are roots of the  equation ${\mathrm{x}}^{2}-12\mathrm{x}+\mathrm{b}=0$ and $\mathrm{\alpha },\mathrm{\beta },\mathrm{\gamma },\mathrm{\delta }$ form an increasing  GP, then the values  of a and b are respectively

1. A

2,16

2. B

4,8

3. C

2,32

4. D

None of these

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

$\because \mathrm{\alpha },\mathrm{\beta },\mathrm{\gamma },\mathrm{\delta }$ are in GP.

Let $\mathrm{\alpha }=\mathrm{A},\mathrm{\beta }=\mathrm{Ar},\mathrm{\gamma }={\mathrm{Ar}}^{2},\mathrm{\delta }={\mathrm{Ar}}^{3}$

$\because$$\mathrm{\alpha }$ and $\mathrm{\beta }$ are the roots of the equation ${\mathrm{x}}^{2}-3\mathrm{x}+\mathrm{a}=0$,
then

On solving Eqs. (i) and (ii), we get

$\mathrm{A}=1,\mathrm{r}=2$  Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)