JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Medium

1 of 1

Analyzing +4 | -1

Let

\alpha, \beta

be the roots of the equation

p x^2+q x+r=0

p \neq 0

. If

p, q, r

are in

\mathrm{AP}

and

\frac{1}{\alpha}+\frac{1}{\beta}=4

, the value of

|\alpha-\beta|

, is

View answer and explanation

Correct option: B

\frac{2 \sqrt{13}}{9}

Option B (

\frac{{2 \sqrt{{13}}}}{{9}}

) is correct because it is the result of calculating the difference between the roots of the quadratic equation given the conditions that p, q, r are in AP and

\frac{{1}}{{\alpha}} + \frac{{1}}{{\beta}} = 4

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