The solutions to \[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$

In decimal form, this is equivalent to 1.25

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Work Shown:

The given equation 2x^2-10x+13 = 0 matches the form ax^2+bx+c = 0

We see that a = 2, b = -10, c = 13. Plug those values into the quadratic formula to solve for x.

The two solutions are in the form where a = 5/2 and b = 1/2

Therefore a*b = (5/2)*(1/2) = 5/4 = 1.25