If the equation $x^{4} - 4 x^{3} + a x^{2} + b x + 1 = 0$ has four roots (all positive), then value of $a$ and $b$ , are given as

a = 4, b = 6

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

a = - 4, b = 6

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

a = 6, b = - 4

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

None of these

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

Open in App

Solution

The correct option is C $a = 6, b = - 4$
Let $f (x) = x^{4} - 4 x^{3} + a x^{2} + b x + 1 = 0$
For $a = 6, b = - 4$
$f (x) = {(x - 1)}^{4}$
Then $1$ is positive root

Suggest Corrections

Similar questions

If the equation $x^{4} - 4 x^{3} + a x^{2} + b x + 1 = 0$ has four roots. All of them are positive real roots then value of a and b are given.

Q. If the equation

x^{4} - 4 x^{3} + a x^{2} + b x + 1 = 0

has four positive roots, then the value of

(a + b)

is:

Q. If

a, b

are real numbers such that

x^{3} - a x^{2} + b x - 6 = 0

has its roots real and positive then the minimum value of

b

is:

If the equation $2 x^{4} + 7 x^{3} + a x + b = 0$ has four roots (All real roots) then find the value of a and b. Given that (x - 3) and (x - 1) may exactly divide the above given expression.

Q. If

2 x^{3} + a x^{2} + b x + 4 = 0

(a and b are positive real numbers) has

3

real roots, then prove that

a + b \geq 6 (2^{1 / 3} + 4^{1 / 3})

Join BYJU'S Learning Program

If the equation x4−4x3+ax2+bx+1=0 has four roots (all positive), then value of a and b, are given as

The correct option is C a=6,b=−4Let f(x)=x4−4x3+ax2+bx+1=0For a=6,b=−4f(x)=(x−1)4Then 1 is positive root

If the equation $x^{4} - 4 x^{3} + a x^{2} + b x + 1 = 0$ has four roots (all positive), then value of $a$ and $b$ , are given as

The correct option is C $a = 6, b = - 4$
Let $f (x) = x^{4} - 4 x^{3} + a x^{2} + b x + 1 = 0$
For $a = 6, b = - 4$
$f (x) = {(x - 1)}^{4}$
Then $1$ is positive root