Question

Find the value of p so that the quadratic equation (p – 5)x2 + 2( p – 5 )x + 2= 0 has two equal roots

Answer 1

Step-by-step explanation:

Explanation

We are given a quadratic equation

(p-5)x^2+2 (p-5)x+2=0

Condition for 2 equal roots.

For the two roots to be equal, the discriminant of the given quadratic equation should be equal to zero

Now on equating the discriminant of the given quadratic equation to zero, we get the desired value of p

Procedure

4 (p-5)^2 - 4 (p-5)(2)=0

4 (p^2+25-10p) - 8p+40=0

ON SOLVING THE ABOVE EQUATION BY SPLITTING THE MIDDLE TERM,

WE GET THE VALUE OF P AS 7