Answer:
q = 2
Explanation:
You want to find q such that the difference between the two roots of 3x²-5x+q is 1/3.
Sum of roots
In quadratic ax²+bx+c, the sum of the roots is (-b/a). For roots p and s, this tells us ...
p + s = -(-5)/3 = 5/3
The problem statement tells us the difference is ...
p - s = 1/3
Adding these two equations gives ...
2p = (5+1)/3 = 2
p = 1 . . . . . . . . . . . . . divide by 2
s = p -1/3 = 2/3 . . . . find the smaller root
Product of roots
The product of the two roots is (c/a) = (q/3):
ps = (1)(2/3) = q/3
q = 2 . . . . . multiply by 3
The value of q is 2.
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