CameraIcon

SearchIcon

MyQuestionIcon

1

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

Global Maxima

If α, β are...

Question

If $α, β$ are the non-zero roots of $a x^{2} + b x + c = 0$ and $α^{2}, β^{2}$ are the roots of $a^{2} x^{2} + b^{2} x + c^{2} = 0$ , then $a, b, c$ are in

A

G . P .

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

B

H . P .

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

C

A . P .

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

D

none of these

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

Open in App

Solution

The correct option is B $G . P .$
From the sum and product property of quadratic equations, we have $α + β = (- b / a)$ ,
$α β = c / a$ from the first equation.
Now, from the second equation, we have $α^{2} + β^{2} = - {(b / a)}^{2}$ ie ${(α + β)}^{2} - 2 α β = - {(b / a)}^{2}$ .
Now, putting the respective values of $α + β$ and $α β$ , we get $b^{2} = a c$ which is the required condition for $G . P$ .

Suggest Corrections

thumbs-up

0

Similar questions

α, β

are the roots of

a x^{2} + b x + c = 0

α + β, α^{2} + β^{2}, α^{3} + β^{3}

are in G.P., where

△ = b^{2} - 4 a c

Q. In the quadratic equation

a x^{2} +

+ c = 0

Δ = b^{2} - 4 a c

α + β, α^{2} + {β^{2}, α}^{3} + β^{3}

are in G.P. where

α, β

are the roots of

a x^{2} +

+ c = 0

α, β

are the roots of

a x^{2} + b x + c = 0

α + β, α^{2} + β^{2}, α^{3} + β^{3}

are in G.P., where

△ = b^{2} - 4 a c

α

β

are the distinct roots of

a x^{2} + b x + c = 0,

a, b

c

are non-zero real numbers then

\frac{a α^{2} + b α + 6 c}{a β^{2} + b β^{2} + 9 c} + \frac{a β^{2} + b β^{2} + 19 c}{a α^{2} + b α + 13 c}

α

β

a x^{2} + b x + c = 0

then the equation whose roots are

α^{2}

β^{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Extrema

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon