Question

If \((x-1)\) is a factor of \(mx^2-\sqrt2 x+1=0\), then the value of 'm' is:

Answer 1

\((x-1)\) is a factor of \(p(x) = mx^2-\sqrt2 x+1=0\).
Using Factor Theorem,
\(p(1) = 0\)
\(m \times 1^2 - \sqrt2 \times 1+1=0\)
\(m -\sqrt2+1=0\)
\(m=\sqrt2-1\)