Question

If one of the roots of 3x²-(4k+1)x+k²+5=0 is one third of the other find k​

Answer 1

Given:

3x²-(4k+1)x+k²+5=0

Find:

Value of k

Solution:

Let a and a/3 are the roots of 3x^2+(1+4k).x+(k^2+5)=0.

⇒ a+a/3=-(1+4k)/3.

⇒ 4a/3= -(1+4k)/3.

⇒ 4a = -(1+4k).

⇒ a =-(1+4k)/4…………….(1)

⇒ a×a/3 =(k^2+5)/3.

⇒ a^2 = (k^2+5).

put a =-(1+4k)/4 from eq .(1).

⇒  {+(1+4k)^2}/16=(k^2+5).

⇒ 1+16k^2+8k = 16k^2+80.

⇒ 8k=79

⇒ k = 79/8

So, the value of k is 79/8

I hope it will help you.

Regards.

Answer 2

Answer:

one of the roots of 3x²-(4k+1)x+k²+5=0 is one third of the other find k