Question

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

Answer 1

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 = $\frac{-b}{a}$

product : αβ  =  $\frac{c}{a}$

α + β = $\frac{--5}{2}$  = $\frac{5}{2}$   = 2.5 -------------------------------------(1)

αβ = $\frac{c}{2}$   -----------------------------------------------------------(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 = $\frac{c}{2}$

1.375 × 1.125  =  $\frac{c}{2}$

1.546875 =  $\frac{c}{2}$

multiply both-side of the equation by 2

1.546875 × 2 = c

3.09375 = c

c = 3.09375