Question

Determine whether the values given against the quadratic equation are the roots of the equation.

2m² – 5m = 0, m = 2, `5/2`

Answer 1

 2m² – 5m = 0,  

\[m = 2, \frac{5}{2}\] 

When m = 2
\[2 \left( 2 \right)^2 - 5\left( 2 \right) = 0\]
\[ \Rightarrow 8 - 10 = 0\]
\[ \Rightarrow - 2 \neq 0\]

So, m = 2 is not a solution of the given equation. 

When \[m = \frac{5}{2}\]
\[2 \left( \frac{5}{2} \right)^2 - 5\left( \frac{5}{2} \right) = 0\]
\[ \Rightarrow \frac{25}{2} - \frac{25}{2} = 0\]
So,

\[m = \frac{5}{2}\] is a solution of the given quadratic equation.
Thus, only \[m = \frac{5}{2}\] is a root of the given quadratic equation.