Question

Find the value of p for p(x)=(p+1)x²-6(p+1)x+3(p+q)=0,has equal roots. Also find the roots

Answer 1

The given equation is a quadratic equation.
The root of a quadratic equation is given by the equation
Also we know that if the roots are equal then =0
(if it is greater than 0,there will be 2 distinct roots,if less than zero then the roots are imaginary)

​​​​​​Let r be the root of the equation, and since the roots are equal

Here b = -6(p+1)
a = p+1
So

So the root of the equation is 3.
A root of an equation means the possible values of x in the equation. So we can substitute x=3 in the equation.Then,

On solving we get,