If a x 2 -bx-c-0 and b x 2 -cx-a-0 have a common root a- 0- then a 3 - b 3 - c 3 abc is equal to

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

Combination

If a x 2 +b...

Question

If $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ have a common root $a \neq 0$ , then $\frac{a^{3} + b^{3} + c^{3}}{a b c}$ is equal to

1

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

2

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

3

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

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 $3$
Given that the equations $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ has a common roots.

According to the condition for common roots, we have

${(b c - a^{2})}^{2} = (c a - b^{2}) (a b - c^{2})$

$\Rightarrow b^{2} c^{2} - 2 a^{2} b c + a^{4} = a^{2} b c - a c^{3} - a b^{3} + b^{2} c^{2}$

$\Rightarrow a^{3} - 2 a b c = a b c - c^{3} - b^{3}$

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

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

Suggest Corrections

Similar questions

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

and

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

have a common root and

a, b,

and

c

are nonzero numbers, then find the value of

(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 is equal to

The correct option is B 3Given that the equations ax2+bx+c=0 and bx2+cx+a=0 has a common roots. According to the condition for common roots, we have(bc−a2)2=(ca−b2)(ab−c2)⇒b2c2−2a2bc+a4=a2bc−ac3−ab3+b2c2⇒a3−2abc=abc−c3−b3⇒a3+b3+c3=3abc⇒a3+b3+c3abc=3

If $a x^{2} + b x + c = 0$ and $b x^{2} + c x + a = 0$ have a common root $a \neq 0$ , then $\frac{a^{3} + b^{3} + c^{3}}{a b c}$ is equal to