If the sum of all the roots and the product of all the roots of a cubic polynomial $3 x^{3} + 5 x^{2} + 6 x + k$ are equal, then the value of k is

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

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

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

Open in App

Solution

The correct option is C 5
Given cubic polynomial is $3 x^{3} + 5 x^{2} + 6 x + k .$
∴ Product of roots is $\frac{- k}{3}$

Sum of roots is $\frac{- 5}{3}$

Now, given that the sum of roots and the product of roots of the cubic polynomial $3 x^{3} + 5 x^{2} + 6 x + k$ are equal.

$∴ \frac{- k}{3} = \frac{- 5}{3}$

$\Rightarrow k = 5$

Hence, the correct answer is option (c).

Suggest Corrections

Similar questions

If 1,m and k are the roots of the cubic polynomial whose sum is 5 and sum of product of roots taken two at a time is 8, then value of (m-k) is,

3 x^{3} + 5 x^{2} + 9 x = 0

f (x) = 5 x^{2} + 13 x + k

f (x) = 5 x^{2} + 13 x + k

5 x^{2} - 2 k x + 20 = 0

k

Join BYJU'S Learning Program