Q.Find the values of m, for which the equation $x^2 - 15 - m(2x - 8) = 0$ have equal roots.

Rewriting the equation in standard quadratic form and setting the discriminant to zero gives $m=3$ or $m=5$.

Step 1 — Rewrite in standard form.

$x^2-15-m(2x-8)=0 \implies x^2-15-2mx+8m=0 \implies x^2-2mx+(8m-15)=0$.

Step 2 — Equal roots condition.

For $ax^2+bx+c=0$ to have equal (repeated) roots, the discriminant $b^2-4ac=0$.

Here $a=1,\ b=-2m,\ c=8m-15$.

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