The correct statement about the roots of the equation $x^{2}$ - 2ax - $b^{2} = 0$ is

Real and equal

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

Real and opposite in sign

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

Imaginary

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

Real and same in sign

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

Open in App

Solution

The correct option is B
Real and opposite in sign

Discriminant = $4 (- 2 a)^{2}$ + 4 $b^{2} = 16 a^{2} + 4 b^{2} △ \geq 0$
$\Rightarrow$ Real Product of the roots = $- b^{2}$
= -ve
$\Rightarrow$ Roots are opposite in sign

Suggest Corrections

Similar questions

The abscissae of A and B are the roots of the equation $x^{2} + 2 a x - b^{2} = 0$ and their coordinates are the roots of the equation $y^{2} + 2 p y - q^{2}$ = 0. The equation of the circle with AB as diameter

Q. If A.M of the roots of

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

is equal to the of the roots of the equation

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

. They are in :

Q. If the abscissa and ordinates of two points

P

and

Q

are the roots of the equations

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

and

x^{2} + 2 p x - q^{2} = 0

respectively, then the equation of the circle with

P Q

as diameter is

Q. Prove that the arithmetic mean of the roots of

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

is equal to the geometric mean of the roots of the equation

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

Q. The roots of the quadratic equation

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

are where a,b,c

\in R :

Join BYJU'S Learning Program

The correct statement about the roots of the equation x2 - 2ax - b2=0 is

The correct option is B Real and opposite in sign Discriminant = 4(−2a)2 + 4 b2=16a2+4b2 △≥0 ⇒ Real Product of the roots = −b2 = -ve ⇒ Roots are opposite in sign

The correct statement about the roots of the equation $x^{2}$ - 2ax - $b^{2} = 0$ is

The correct option is B
Real and opposite in sign

Discriminant = $4 (- 2 a)^{2}$ + 4 $b^{2} = 16 a^{2} + 4 b^{2} △ \geq 0$
$\Rightarrow$ Real Product of the roots = $- b^{2}$
= -ve
$\Rightarrow$ Roots are opposite in sign