If a x2-b x-c-0 and b x2-c x-a-0 have a common root a - 0- then a3-b3-c3-a b c-A- 2B- 4C- 3D- 1

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

Byju's Answer

Standard XII

Mathematics

Sum of n Terms

If a x2+b x+c...

Question

If $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ have a common root

a ≠ 0, then $\frac{a^{3} + b^{3} + c^{3}}{a b c} =$

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

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

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

Open in App

Solution

The correct option is C
3

The condition for common roots gives $(b c - a^{2})^{2} = (c a - b^{2}) (a b - c^{2})$ On simplification gives $a^{3} + b^{3} + c^{3} = 3 a b c$

Suggest Corrections

Similar questions

Q. If

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

and

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

have a common root and

a \neq 0

, then

\frac{a^{3} + b^{3} + c^{3}}{a b c} =

Q. The equation

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

have a common root then

\frac{a^{3} + b^{3} + c^{3}}{a b c}

If $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ have a common root

a ≠ 0, then $\frac{a^{3} + b^{3} + c^{3}}{a b c} =$

If $a x^{2} + b x + c = 0 a n d b x^{2} + c x + a = 0$ have a common root and a,b,c are non - zero real numbers then $\frac{a^{3} + b^{3} + c^{3}}{a b c}$ is equal to :

Q. If

a, b, c

are non-zero real numbers and

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

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

have one root in common, then

\frac{a^{3} + b^{3} + c^{3}}{a b c} =

Join BYJU'S Learning Program

If ax2+bx+c=0 and bx2+cx+a=0 have a common root a ≠ 0, then a3+b3+c3abc=

The correct option is C 3 The condition for common roots gives (bc−a2)2=(ca−b2)(ab−c2) On simplification gives a3+b3+c3=3abc

If $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ have a common root

a ≠ 0, then $\frac{a^{3} + b^{3} + c^{3}}{a b c} =$

The correct option is C
3

The condition for common roots gives $(b c - a^{2})^{2} = (c a - b^{2}) (a b - c^{2})$ On simplification gives $a^{3} + b^{3} + c^{3} = 3 a b c$