If x1 and x2 are the roots of ax2-bx-c-0- b 0 and they are of opposite sign- then the roots of x1x-x22-x2x-x12-0 are

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

Location of Roots

If x1 and x2 ...

Question

If $x_{1}$ and $x_{2}$ are the roots of $a x^{2} + b x + c = 0, b \neq 0$ and they are of opposite sign, then the roots of $x_{1} (x - x_{2})^{2} + x_{2} (x - x_{1})^{2} = 0$ are

real

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

non real

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

of same sign

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

of opposite sign

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

Open in App

Solution

The correct options are
A real
D of opposite sign
Since, roots are opposite in sign.
Therefore, $x_{1} x_{2} < 0$
$x_{1} (x - x_{2})^{2} + x_{2} (x - x_{1})^{2} = 0$
$\Rightarrow (x_{1} + x_{2}) x^{2} - (4 x_{1} x_{2}) x + x_{1} x_{2} (x_{1} + x_{2}) = 0$
Now,
$D = 16 (x_{1} x_{2})^{2} - 4 x_{1} x_{2} (x_{1} + x_{2})^{2} ∴ D > 0 (∵ x_{1} x_{2} < 0)$

The product of roots is
$= \frac{x_{1} x_{2} (x_{1} + x_{2})}{(x_{1} + x_{2})} = x_{1} x_{2} < 0$

Hence, the roots are real and of opposite sign.

Suggest Corrections

Similar questions

Let $x_{1}, x_{2}$ be the roots of $a x^{2} + b x + c = 0$ and $x_{1} . x_{2} < 0$ , $x_{1} + x_{2}$ is non - zero. Roots of $x_{1} (x - x_{2})^{2} + x_{2} (x - x_{1})^{2} = 0$ are

x_{1}

and

x_{2}

are the real roots of

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

and

x_{1} x_{2} < 0

. The roots of

x_{1} (x - x_{2})^{2} + x_{2} (x - x_{1})^{2} = 0

are

Q. For the quadratic equation

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

, if

b^{2} - 4 a c > 0

and

a, c

have same sign, then which of the following is true?

(a, b, c \in R, a \neq 0)

Q. If

α, β

are roots of equation

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

which are real and opposite in sign, then roots of the equation

α {(x - β)}^{2} + β {(x - α)}^{2} = 0

are

Join BYJU'S Learning Program

Explore more

Location of Roots

Standard XIII Mathematics

Join BYJU'S Learning Program

If x1 and x2 are the roots of ax2+bx+c=0,b≠0 and they are of opposite sign, then the roots of x1(x−x2)2+x2(x−x1)2=0 are

If $x_{1}$ and $x_{2}$ are the roots of $a x^{2} + b x + c = 0, b \neq 0$ and they are of opposite sign, then the roots of $x_{1} (x - x_{2})^{2} + x_{2} (x - x_{1})^{2} = 0$ are