CameraIcon

SearchIcon

MyQuestionIcon

1

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

Constant Function

One root of ...

Question

One root of $x^{3} - 3 x^{2} + 4 x - 1 = 0$ lies between

A

0 and 1

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

B

1 and 2

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

C

2 and 3

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

D

4 and 5

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

Open in App

Solution

The correct option is A 0 and 1
Let $f (x) = x^{3} - 3 x^{2} + 4 x - 1$
$f^{'} (x) = 3 x^{2} - 6 x + 4 > 0 \forall x ϵ R$
Hence f is increasing function
Now $f (0) < 0, f (1) > 0, f (2), f (3), f (4), f (5) > 0$
Hence one root of f will definitely lie in (0,1).

Suggest Corrections

thumbs-up

0

Similar questions

Q. If the roots of

x^{3} + 3 x^{2} + 4 x - 11 = 0

a, b

c

x^{3} + r x^{2} + s x + t = 0

a + b, b + c

c + a

, then the value of

t

Which of the following point lies on lines 2x + 5y = -11 and 4x + 10y = -22?

Q. Assertion (A) : One root of

x^{3} - 2 x^{2} - 1 = 0

lies between 2 and 3.
Reason (R) : If

f (x)

is continuous function and

f (a), f (b)

have opposite sings then atleast one root of

f (x) = 0

a

b

.

Q. If the quadratic equation

3 x^{2} + 4 x + 5 = 0

α

β

then the equation whose roots are

\frac{1}{α}

\frac{1}{β}

Q. The set of all values of

k > - 1,

for which the equation

(3 x^{2} + 4 x + 3)^{2} - (k + 1) (3 x^{2} + 4 x + 3) (3 x^{2} + 4 x + 2) + k (3 x^{2} + 4 x + 2)^{2} = 0

has real roots, is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Some Functions and Their Graphs

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Constant Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon