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Answer: c. between 0&1 and 2&3
Step-by-step explanation:
We want to find the roots of :
y = 2x^2 5x + 1
we can use the Bhaskara equation and find that:
and 4*4 = 16
5*5 = 25
then √18 is a number between 4 and 5.
So the roots are:
x = (5 +√18 )/4 = is a number larger than 2 but smaller than 3 (it can not be bigger than 3 because we know that √18 is smaller than 5, suppose it is equal to 5, then (5 + 5)/4 = 10/4, that is smaller than 3)
2 < (5 +√18 )/4 < 10/4 < 3
x = (5 - √18)/4 = is a number smaller than 1 and bigger than zero (because √18 is smaller than 5 so the number in the parentheses never can be 0, and √18 is bigger than 4, if we take this value we have that:
(5 - 4)/4 = 1/4 = 0.25
then we have: 0 < (5 - √18)/4 < 1/4 < 1
So one root is between 0 and 1, and the other root is between 2 and 3.