Question

Solve: $\frac{4t}{t^2-25}=\frac{1}{5-t}$

• A.
  5
• B.
  -1
• C.
  -5
• D.
  1
• E.
  5 or -1

Answer 1

The correct option is E

5 or -1
Cross multiply and we get 4t (5 -t) = $t^2$ - 25
$\Rightarrow$ 20t - 4$t^2$ = $t^2$ - 25 $\Rightarrow$ 5$t^2$ - 20t - 25 = 0
$\Rightarrow$ $t^2$ - 4t - 5 = 0
Let p and q be the roots of the equation.
Then, sum of the roots, p + q = -$\frac{-4}{1}=4$
Product of the roots. pq = -5
So, t can be either 5 or -1