Question

The product of all roots of the equation \((x^2-5x+7)^2 - (x-2)(x-3)=1\) is

Answer 1

Given equation is
\((x^2-5x+7)^2 - (x-2)(x-3)=1\\
\Rightarrow (x^2-5x+7)^2 - (x-2)(x-3)-1 = 0\)
The given equation will be of form
$x^4+bx^3+cx^2+dx+e = 0$
So, the product of the roots $=e$
Putting $x = 0$, we get the value of $e$
$e = (7)^2 - (-2)(-3)-1 = 42$
\(\therefore\) Product of the roots
\(~~~=7 \times 6=42\)