If one root of the quadratic equation ax 2- bx - c -0 - a - b - c - R is reciprocal of the other- then which one of the following is correct-A- a-b-0 B- b - cC- a - CD- a-c-0

The correct option is D a+c=0ax^2 bx c=0; a,b,c∈ℝ Since, this is a quadratic equation, so a0. Let the roots be α and 1α. So, product of roots is, α×1α= ca ⇒ a ...

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Nature of Roots

If one root o...

Question

If one root of the quadratic equation $a x^{2} - b x - c = 0; a, b, c \in R$ is reciprocal of the other, then which one of the following is correct?

a + b = 0

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

b = c

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

a = c

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

a + c = 0

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

Open in App

Solution

The correct option is D $a + c = 0$
$a x^{2} - b x - c = 0; a, b, c \in R$
Since, this is a quadratic equation, so $a \neq 0$ .
Let the roots be $α$ and $\frac{1}{α}$ .
So, product of roots is,
$α \times \frac{1}{α} = - \frac{c}{a}$
$\Rightarrow a = - c$
$\Rightarrow a + c = 0$

Suggest Corrections

Similar questions

If one root of polynomial equation ax² + bx + c = 0 be reciprocal of other, then

Q. If one root of the quadratic equation

a x^{2} - b x - c = 0; a, b, c \in R

is reciprocal of the other, then which one of the following is correct?

Q. Let

△ P Q R

be a right triangle, right angled at

R .

tan (\frac{P}{2})

and

tan (\frac{Q}{2})

are the roots of the quadratic equation

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

, then which of the following is correct ?

Q. The roots of the equation ax2 + bx + c =0 will be reciprocal of each other if
(a) a=b
(b) c=a
(c) b=c
(d) b=0

If a, b, c $\in$ R and a $\neq$ 0, c < 0, and if the quadratic equation $a x^{2} + b x + c$ = 0 has imaginary roots, then a + b + c is

Join BYJU'S Learning Program

Explore more

Nature of Roots

Standard XII Mathematics

Join BYJU'S Learning Program

If one root of the quadratic equation ax2−bx−c=0; a,b,c∈R is reciprocal of the other, then which one of the following is correct?

The correct option is D a+c=0ax2−bx−c=0; a,b,c∈R Since, this is a quadratic equation, so a≠0. Let the roots be α and 1α. So, product of roots is, α×1α=−ca ⇒a=−c ⇒a+c=0

If one root of the quadratic equation $a x^{2} - b x - c = 0; a, b, c \in R$ is reciprocal of the other, then which one of the following is correct?

The correct option is D $a + c = 0$
$a x^{2} - b x - c = 0; a, b, c \in R$
Since, this is a quadratic equation, so $a \neq 0$ .
Let the roots be $α$ and $\frac{1}{α}$ .
So, product of roots is,
$α \times \frac{1}{α} = - \frac{c}{a}$
$\Rightarrow a = - c$
$\Rightarrow a + c = 0$