If ax2 -bx-c-0 and bx2-cx-a-0 have a common roota - 0- then a3-b3-c3-abc -

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Standard XII

Mathematics

Common Roots

If ax2 +bx+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 $\frac{a^{3} + b^{3} + c^{3}}{a b c} =$

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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 $a^{3} + b^{3} + c^{3} = 3 a b c$

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Similar questions

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}

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} =

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

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

Q. If

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

have common root

1

and

a, b, c

are zero real no. then find the value of

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

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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 $a^{3} + b^{3} + c^{3} = 3 a b c$