JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Medium

1 of 1

Analyzing +4 | -1

If the sum of the roots of the equation

a x^2+b x+c=0

equal to the sum of the reciprocals of their squares. Then

\frac{a}{c}, \frac{b}{a}, \frac{c}{b}

are in

View answer and explanation

Correct option: C

H.P

Option C (H.P) is correct because after manipulating the given equation and simplifying, the resulting terms are in Arithmetic Progression, which implies the reciprocals are in Harmonic Progression.

More Questions from THEORY OF EQUATION

Practice All Chapter MCQs →

The maximum number of real roots of the equation

{x^{2n}} - 1 = 0

is The number of roots of the equation

\frac{1}{x}+\frac{1}{\sqrt{\left(1-x^2\right)}}=\frac{35}{12}

is How many real solutions does the equation

x^7+14 x^5+16 x^3+30 x-560=0

have? If

x_1, x_2, x_3, \ldots, x_n

are the roots of the equation

x^n+a x+b=0

, the value of

\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_1-x_4\right) \ldots\left(x_1-x_n\right)

is The polynomials

P(x)=k x^3+3 x^2-3

and

Q(x)=2 x^3-5 x+k

, when divided by

(x-4)

leave the same remainder, then

k

is equal to: If

{\left( {x - 1} \right)^3}

is a factor of

{x^4} + a{x^3} + b{x^2} + cx - 1,

then the other factor is