Question

If 5 is a root of the quadratic equation 5x^2 - (2-3p)r 15 = 0 and the quadratic equation
2 px^2+pr+k=0, has equal roots, then find the value of p and k

Answer 1

Answer:

Kindly refer to this attachment

Answer 2

Answer:

Step-by-step explanation:

begin mathsize 16px style Given space that space px squared space – space 2 square root of 5 space px space plus space 15 space equals space 0 space has space equal space roots.

Let space straight a equals straight p comma space straight b equals space – space 2 square root of 5 space straight p comma space straight c equals 15

Since space the space equation space has space equal space roots comma space straight b squared minus 4 ac equals 0

rightwards double arrow space open parentheses – space 2 square root of 5 space straight p close parentheses squared minus 4 left parenthesis straight p right parenthesis left parenthesis 15 right parenthesis equals 0

rightwards double arrow 20 straight p squared minus 60 straight p equals 0

rightwards double arrow 20 straight p left parenthesis straight p minus 3 right parenthesis equals 0

rightwards double arrow 20 straight p equals 0 space space or space straight p minus 3 equals 0

rightwards double arrow straight p equals 0 space or space straight p equals 3

If space we space substitute space straight p equals 0 space back space in space the space original space equation comma space we space do space not space get space an space equation.

So comma space straight p equals 3.