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

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

Integration by Partial Fractions

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

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

N . O . T

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

Open in App

Solution

The correct option is D $3$
Given,

$f (x) = a x^{2} + b x + c$

$g (x) = b x^{2} + c x + a$

If we set $t$ as the common root, then we know that $f (t) = g (t) = 0$ :

$a t^{2} + b t + c = b t^{2} + c t + a$

We can equate coefficents to conclude that $a = b = c$

Therefore, we can say that

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

Suggest Corrections

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}

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

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 and a≠0, then a3+b3+c3abc=

The correct option is D 3Given,f(x)=ax2+bx+cg(x)=bx2+cx+aIf we set t as the common root, then we know that f(t)=g(t)=0:at2+bt+c=bt2+ct+aWe can equate coefficents to conclude that a=b=cTherefore, we can say thata3+b3+c3abc=a3+a3+a3aaa=3a3a3=3

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