# If cos^4 theta+alpha , sin^4 theta +alpha are the roots of the equation x^2+b(2x+1) =0 and cos^2 theta +beta ,sin^2 theta +beta are the roots of the equation x^2+4x+2=0 then b is equal to

Solution:   We have ,

$\cos^{4}\theta+\alpha , \sin^{4}\theta+\alpha$   are the roots $x^{2}+b(2x+1)=0$

$\cos^{2}\theta+\beta ,\sin^{2}\theta+\beta$   are the roots    $x^{2}+4x+2=0$

$\Rightarrow$     $\cos^{4}\theta-\sin^{4}\theta=\cos^{2}\theta-\sin^{2}\theta=\cos 2\theta$

$\Rightarrow$                       $(-2b)^{2}-4b=(-4)^{2}-4\times 2$

$\Rightarrow$                       $b^{2}-b-2=0\Rightarrow b=-1,2$

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
##### Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout NEET (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-