Q)  Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots.

Ans: 

Given quadratic equation is:

px (x – 2) + 6 = 0

or we can rewrite it as, px² – 2p x + 6 = 0

In this equation, we can see that a = p, b = – 2p and c = 6

Since it is given that the equation has two equal roots,

   D = 0

or b² – 4ac = 0

Substituting the values of a, b and c, we get:

(-2p)² – 4(p)(6) = 0

4p² – 24p = 0

4p(p – 6) = 0

p = 0, p = 6

Since p ≠ 0, Hence, p = 6.

Therefore, for p = 6, the given quadratic equation will have equal roots

Check: let’s put the value p = 6 in the quadratic equation and check if we get 2 equal roots:

px (x-2) + 6 = 0

6x (x-2) + 6 = 0

x (x-2) + 1 = 0

x²  – 2 x + 1 = 0

(x-1)² = 0

It gives two equal roots of x = 1.