Question

If both the roots of

2 2 K x r x x (6 3) 2 1 0

and

2 2 6 (2 1) 4 2 0 K x p x x

are common,

then the value of

2r p

is​

Answer 1

Question:-

⇒ If both the roots of K(6x^2 + 3 ) + rx + 2x^2 - 1 = 0 and 6K(2x^2 + 1) + p x + 4x^2 - 2 = 0  are common , then the value of $2r - p$ is ?

Answer:-

⇒ x^2(6K +2) + r x + ( 3K - 1) = 0 --------(1)

⇒ & x^2(12K + 4 ) + P x + ( 6K - 2 ) = 0 ------(2)

dividing equation (2)by 2

We get :-

⇒ x^2 ( 6K + 2) + P x/2 + ( 3K-1) =  0 ----(3)

therefore :-

from (1 ) & (3) By comparing

r = p/2

2r =  p

2r - p = 0

so your answer is zero.