Mathematics - Quadratic Equation Question with Solution | TestHub

$|x-p|=x-p$ (Since $x\ge p$)

$|x-15|=15-x$ (Since $x\le 15$)

$|x-(p+15)|=(p+15)-x$ (as $15+p>x$)

Therefore, the expression reduces to $E=x-p+15-x+p+15-x$.

$E=30-x$

Therefore, $E_{min}$ occurs when $x=15$.

Thus, $\lambda =15$.