Question

The difference between the roots of the equation 2x2−5x+c=0 is 0.25. Find c.

Answer 1

c = 3.09375

Explanation:

let the roots be α and β

2x2−5x+c=0

Comparing withe the standard equation ax² + bx + c = 0

a=2 b = -5 and c=c

sum : α + β =
`(-b)/(a)`

product : αβ =
`(c)/(a)`

α + β =
`(--5)/(2)` =
`(5)/(2)` = 2.5 -------------------------------------(1)

αβ =
`(c)/(2)` -----------------------------------------------------------(2)

the question says "the difference between the roots of the equation is 0.25"

so, α -β = 0.25 ---------------------------------------------------(3)

we can use equation (1) and equation (3) to find the values of our α and β by solving simultaneously

add equation (1) and equation (3)

2 α = 2.75

α = 2.75 /2 = 1.375

subtract equation (3) from equation (1)

2β = 2.25

β = 2.25 /2 = 1.125

we can now use equation (2) to find the value of c

αβ =
`(c)/(2)`

1.375 × 1.125 =
`(c)/(2)`

1.546875 =
`(c)/(2)`

multiply both-side of the equation by 2

1.546875 × 2 = c

3.09375 = c

c = 3.09375