Question

2m²-5m=0,m=2, 5/2 determine whether the value given against of the quadratic equation are the root of the equation. ​

Answer 1

p(X)=2m²-5m

g(X)=m-2

m-2=0

m=2

p(2)=2*2*2-5*2

=8-10

=-2

since remainder is not 2, m-2 is not a factor by factor theorem.

2nd case

g(X)=2m-5

2m-5=0

m=5/2

p(5/2)=2*5/2*5/2-5*5/2

=25/2-25/2=0

therefore, 2m-5 is a factor by factor theorem.

hence, 5/2 is a root and 2is not a root

Answer 2

$p(m) = 2m {}^{2} - 5m \\ g(m) = 2 \: and \: \frac{5}{2} \\ p(2) = (2 \times 2 {}^{2}) - (5 \times 2) \\ = (2 \times 4) - 10 \\ = 8 - 10 = - 2 \: ans... \\ p( \frac{5}{2} ) = (2 \times \frac{5}{2} ) - (5 \times \frac{5}{2} ) \\ = 5 - \frac{25}{2} = \frac{10 - 25}{2} \\ \frac{ - 15}{2} ans...$