CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Quadratic Equations

If α β ...

Question

If $α$ & $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0,$ where $c < 0 < b$ , then

A

0 < α < β

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

B

α < 0 < β < | α |

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

C

α < β < 0

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

D

α < 0 < | α | < β

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

Open in App

Solution

The correct option is B $α < 0 < β < | α |$
$α + β = (\frac{- b}{1}) = - v e h e n c e e i t h e r b o t h r o o t s a r e n e g a t i v e o r o n e i s - v e a n d m a g n i t u d e g r e a t e r t h a n$
$t h e + v e r o o t . n o w$
$α + β = (\frac{c}{1}) = - v e$
Hence it is confirmed that one
$r o o t i s - v e a n d o t h e r a r e i s + v e$
$∴ α < 0 b u t | α | > β ∴ α < 0 < β < | α |$

Suggest Corrections

thumbs-up

0

Similar questions

α

β

(α < β)

, are the roots of the equation

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

c < 0 < b

Q. Statement I: lf

α, β

are the roots of

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

, then the equation whose roots are

\frac{α + β}{α}, \frac{α + β}{β}

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

Statement II: lf

α, β

are the roots of

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

α + h, β + h

are the roots of

x^{2} + q x + r = 0

h = b - q

.
Which of the above statement(s) is(are) true.

α, β

are the roots of quadratic equation

a x^{3} + b x + c = 0

, then find the value of

\frac{α}{β} + \frac{β}{α}

α, β

are the roots of the equation

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

, then form an equation whose roots are:

\frac{α}{β}, \frac{β}{α}

If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ such that $β < α < 0,$ then the quadratic equation whose roots are $| α |, | β |$ is given by

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Quadratic Equations

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon