CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Number Theory: Interesting Results

One root of ...

Question

One root of $a x^{4} + b x^{3} + c x^{2} + d x + e = 0$ , where $a, b, c, d, e$ are rational numbers, is $\sqrt{2} + \sqrt{3}$ , then the other real roots are:

A

\sqrt{2} - \sqrt{3}, 2, 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\sqrt{2} - \sqrt{3}, - 2, 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\sqrt{2} - \sqrt{3}, - \sqrt{2} + \sqrt{3}, 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\sqrt{2} - \sqrt{3}, - \sqrt{2} + \sqrt{3}, - \sqrt{2} - \sqrt{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C $\sqrt{2} - \sqrt{3}, - \sqrt{2} + \sqrt{3}, - \sqrt{2} - \sqrt{3}$
$C o e f f i c i e n t s a r e r a t i o n a l, h e n c e a l l t h e i r r a t i o n a l i t i e s m u s t b e c a n c e l l e d H e n c e t h e r o o t s a r e \sqrt{2} + \sqrt{3}, \sqrt{2} - \sqrt{3}, - \sqrt{2} + \sqrt{3}, - \sqrt{2} - \sqrt{3}$

Suggest Corrections

thumbs-up

0

Similar questions

\sqrt{5} - i \sqrt{7}

a x^{4} + b x^{3} + c x^{2} + d x + e = 0

a, b, c, d, e

are rational numbers, then the other roots are:

2, 5, 7, - 4

are the roots of

a x^{4} + b x^{3} + c x^{2} + d x + e = 0

then the roots of

a x^{4} - b x^{3} + c x^{2} - d x + e = 0

x^{3} + 1

a x^{2} + b x^{3} + c x^{2} + d x + e,

ϵ R a n d a \neq 0,

then the real root of

a x^{4} + b x^{3} + c x^{2} + d x + e = 0

other than -1 is

a, b, c, d, e

are real numbers,show that the roots of

x^{5} + a x^{4} + b x^{3} + c x^{2} + d x + e = 0

cannot all be real, if

2 a^{2} < 5 b

.

3 + 4 i

x^{2} + A x + B = 0

\sqrt{3} - 2

x^{2} + C x + D = 0

A, B, C

D

are all rational numbers, then

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Revisiting Irrational Numbers

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Number Theory: Interesting Results

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon