MyQuestionIcon

1

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

Roots under Different Values of Coefficients

For the equat...

Question

For the equation $x^{2} + b x + c = 0,$ if $1 + b + c = 0$ for all $b, c \in R,$ then roots are

A

\frac{1}{c}

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

B

b

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

C

c

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

D

1

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

Open in App

Solution

The correct option is D $1$
If $a x^{2} + b x + c = 0$ be a quadratic & $a + b + c = 0,$ then $x = 1$ is one solution & the other solution will be $\frac{c}{a}$

$x^{2} + b x + c = 0$ and $1 + b + c = 0$
$\Rightarrow x = 1 & x = c$ are two solutions

Suggest Corrections

thumbs-up

0

Similar questions

Q. For the equation

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

1 + b + c = 0

b, c \in R,

Q. For the equation

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

1 + b + c = 0

b, c \in R,

then the roots are

Q. For the equation

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

1 + b + c = 0

b, c \in R,

Q. If roots of equation

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

, are real & distinct then the roots of equation

2 {c x}^{2} + (b - 4 c) x + 2 c - b + 1 = 0

Q. Assertion :If the equation

a x^{2} + b x + c = 0, (a, b, c \in R, a \neq 0)

x^{2} + 2 x + 3 = 0

have a common root , then

a : b : c

1 : 2 : 3

. Reason: The roots of the equation

x^{2} + 2 x + 3 = 0

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Roots under Different Values of Coefficients

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon