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