MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Quantitative Aptitude

Quadratic Equations

If α and β ar...

Question

If $α a n d β$ are the roots of the equation $x^{2} - 2 x + 4 = 0,$ then what is the value of $α^{3} + β^{3} ?$

A

16

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

B

-16

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

C

8

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

D

-8

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

Open in App

Solution

The correct option is B -16
$(α + β)$ = 2 and $α β = 4$
Use $α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β)$ = 8 - 24 = -16

Suggest Corrections

thumbs-up

0

Similar questions

α, β

are the roots of the equation

x^{2} + 2 x - 15 = 0

then find the values of

α^{3} + β^{3}

α, β

are the roots of the equation

x^{2} - 5 x + 6 = 0

, then the value of

α^{3} + β^{3}

α, β

are the roots of the equation

x^{2} - 2 x + 3 = 0

, then the equation whose roots are

α^{3} - 3 α^{2} + 5 α - 2

β^{3} - β^{2} + β + 5

α

β

are the roots of the equation

x^{2} - 4 x + 1 = 0

(α > β),

then the value of

f (α, β) = \frac{β^{3}}{2} {cosec}^{2} (\frac{1}{2} {tan}^{- 1} \frac{β}{α}) + \frac{α^{3}}{2} {sec}^{2} (\frac{1}{2} {tan}^{- 1} \frac{α}{β})

α

β

are the roots of

x^{2} + p x + q = 0

, then the value of

α^{3} + β^{3}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Quadratic Equations

QUANTITATIVE APTITUDE

Watch in App

explore_more_icon

Explore more

Quadratic Equations

Other Quantitative Aptitude

Join BYJU'S Learning Program

CrossIcon