MyQuestionIcon

1

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

Algebra of Limits

If α and ...

Question

If $α$ and $β$ are the roots of the equation $x^{2} - 6 x + 6 = 0$ , what is $α^{3} + β^{3} + α^{2} + β^{2} + α + β$ equal to?

A

150

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

B

138

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

C

128

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

D

124

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

Open in App

Solution

The correct option is B $138$
Given quadratic equation is $x^{2} - 6 x + 6 = 0$
$α + β = 6, α β = 6$
We know $α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β)$
$= 6^{3} - 3 \times 6 \times 6$
$= 216 - 108 = 108$
Also $α^{2} + β^{2} = (α + β)^{2} - 2 α β = 6^{2} - 2 \times 6 = 36 - 12 = 24$
Thus the value of $(α^{3} + β^{3}) + (α^{2} + β^{2}) + (α + β)$ is $108 + 24 + 6 = 138$ .

Suggest Corrections

thumbs-up

0

Similar questions

α, β

are the roots of

x^{2} - x + 1 = 0

\frac{{(α^{2} - α)}^{3} + {(β^{2} - β)}^{3}}{(2 - α) (2 - β)}

α + β + γ = 2, α^{2} + β^{2} + γ^{2} = 6

α^{3} + β^{3} + γ^{3} = 8

, then the equation whose roots are

α, β, γ

α

β

are the roots of

x^{2} + 5 x - = 0

α^{3} + β^{3}

α^{2} + β^{2}

α

β

are roots of the equation,

x^{2} - 4 \sqrt{2} k x + 2 e^{4 ln k} - 1 = 0

k

α^{2} + β^{2} = 66

α^{3} + β^{3}

α, β

are the roots of the equation

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

{log}_{e} (1 + p x + q x^{2}) = (α + β) x - \frac{α^{2} + β^{2}}{2} x^{2} + \frac{α^{3} + β^{3}}{3} x^{3} + . . .

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebra of Limits

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Algebra of Limits

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon