Question

Without solving the following quadratic equation, find the value of p for which the roots are equal:
$p{x}^2-4x+3=0$

Answer 1

We have
$p{x}^2-4x+3=0$
Comparing it with
$a{x}^2+bx+c=0$,
we get a = p, b = -4 and c = 3.
Now for equal roots,
$b^2-4ac=0\Rightarrow (-4{)}^2-4\times p\times 3=0$
$\Rightarrow 16-12p=0\Rightarrow 12p=16$
$\Rightarrow p=\frac{16}{12}=\frac{4}{3}$.