Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

If one root of $ax^{2}+2bx+c= 0$ is double of other then

Option 1)
$9b^{2}= 8ac$

Option 2)
$8b^{2}= 9ac$

Option 3)
$8a^{2}= 9bc$

Option 4)
$8c^{2}= 9ab$

Answers (1)

Let $\alpha$ & $2\alpha$ are roots of equation

$\therefore \alpha +2\alpha =\frac{-2b}{a}\: \Rightarrow \: 3\alpha =\frac{-2b}{a}\: \Rightarrow \: \alpha =\frac{-2b}{3a}$

$\because \: \alpha$ is root of quadratic , So it will satisfy the equation.

$a\left ( \frac{4b^{2}}{9a^{2}} \right )-\frac{4b^{2}}{3a}+c=0$

$\Rightarrow \: c=\frac{4b^{2}}{3a}-\frac{4b^{2}}{9a}\: \Rightarrow \: c=\frac{8b^{2}}{9a}$

$\Rightarrow \: 8b^{2}=9ac$

$\therefore$ Option (B)

Sum of Roots in Quadratic Equation -

$\alpha +\beta = \frac{-b}{a}$

- wherein

$\alpha \: and\beta$ are root of quadratic equation

$ax^{2}+bx+c=0$

$a,b,c\in C$

Option 1)

$9b^{2}= 8ac$

This is incorrect

Option 2)

$8b^{2}= 9ac$

This is correct

Option 3)

$8a^{2}= 9bc$

This is incorrect

Option 4)

$8c^{2}= 9ab$

This is incorrect

Posted by

subam

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024: NTA debars 39 candidates for 3 years on account of using unfair means

anam-khan

JEE Main 2024 session 2 paper 2 answer key objection window closes today; fees

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’

Latest Question