Question

find the value of m if one root of equation 2x2-8x-m=0 is 5/2

Answer 1

The one root of the equation is 5/2.
hence,it satisfied the given equation.
2x^2- 8x-m = 0
2(5/2)^2-8(5/2)-m = 0
25/2 - 20 - m = 0
25/2 - 20 = m
(25-40)/2 = m
-15/2 = m

i.e. m = -15/2

Answer 2

The value of m is $\bold{\frac{-15}{2}}$.  

Given:

Quadratic equation: $2 x^{2}-8 x-m=0$

One of the root $=\frac{5}{2}$

To find:  

The value of m if one root of equation $2 x^{2}-8 x-m=0 \text { is } \frac{5}{2}$

Solution:  

Substitute $x=\frac{5}{2}$ in the given ‘quadratic equation’

$2\left(\frac{5}{2}\right)^{2}-(8)\left(\frac{5}{2}\right)-\mathrm{m}=0$

$\left(\frac{25}{2}\right)-(4)(5)-\mathrm{m}=0$

$\left(\frac{25}{2}\right)-(20)-\mathrm{m}=0$

$\left(\frac{25}{2}\right)-(20)=\mathrm{m}$

$m=\left(\frac{25-40}{2}\right)$

$m=\frac{-15}{2}$

A quadratic equation expressed as a product of two solutions. If there is ‘no real solution’, there are two ‘complex solutions’. Every quadratic equation, there can be one or more than one solution. These are called the “roots of the quadratic equation”.