If the quadratic equation px2 – 2 root5 px + 15 = 0 has two equal roots,
then find the value of p.

Asked by krishan_5 | 23rd Jan, 2017, 10:26: PM

Expert Answer:

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. end style

Answered by Rebecca Fernandes | 24th Jan, 2017, 09:02: AM