Question

find the values of p for which the roots are real and equal px^2-2x(2p-1)x + 4=0​

Answer 1

Hie!!

For real and equal roots Descrimnant is equal to zero.

Given Quadratic Equation is

px² - 2(2p-1)x+ 4 = 0

It's Descrimnant = (-2(2p-1))² -4(p)(4)

Descrimnant = 4 { 4p² + 1 -4p - 4p }

For real and equal roots Descrimnant = 0

4 { 4p² - 4p + 1 - 4p } = 0

4p² - 8p + 1 = 0

p ={ 8 ± √(64-16) }/8

p = { 8 ±√(48) }/8

p = { 2 ± √3 }/2

p = ( 2 + √3 ) /2

OR

p = ( 2 - √3 )/2