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

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 =

product : αβ  =  

α + β =  =   = 2.5 -------------------------------------(1)

αβ =   -----------------------------------------------------------(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 =

1.375 × 1.125  =  

1.546875 =  

multiply both-side of the equation by 2

1.546875 × 2 = c

3.09375 = c

c = 3.09375

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

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