Answer:
c = 3.09375
Step-by-step 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 = [tex]\frac{-b}{a}[/tex]
product : αβ = [tex]\frac{c}{a}[/tex]
α + β = [tex]\frac{--5}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 -------------------------------------(1)
αβ = [tex]\frac{c}{2}[/tex] -----------------------------------------------------------(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 = [tex]\frac{c}{2}[/tex]
1.375 × 1.125 = [tex]\frac{c}{2}[/tex]
1.546875 = [tex]\frac{c}{2}[/tex]
multiply both-side of the equation by 2
1.546875 × 2 = c
3.09375 = c
c = 3.09375
