Question

For each equation given below, find the value (s) of $p$ so that the equation has equal roots:

$2x^2-7x+p=0$

Answer 1

Step 1: Solve for discriminant.

The given equation is as follows:

$2x^2-7x+p=0$

Compare the given quadratic equation with $a{x}^2+bx+c=0$ to get:

$a=2,b=-7,c=p$

Now, discriminant can be calculated as:

, $\begin{array}{rcl}& \Rightarrow & D=b^2-4ac\\ & =& {\left(-7\right)}^2-4\times 2\times p\\ & =& 49-8p\end{array}$

Step 2: Apply the condition for equal roots.

For equal roots,

$\begin{array}{rcl}{b}^2-4ac& =& 0\\ 49-8p& =& 0\\ 49& =& 8p\\ p& =& \frac{49}{8}\\ p& =& 6\frac{1}{8}\end{array}$

Thus for $p=6\frac{1}{8}$, the equation has equal roots.