PLEASE HELP!

The roots are (15 +/- sqrt(145))/10, and 1/a + 1/b = 7/5.

Let a and b be the solutions to $5x^2-11x+4=0$. Find $1/a + 1/b$ .

According to Vieta's Formula, the sum of the two roots are $-b/a$ and the product of the roots is $c/a$ for an equation in the form of$ax^2+bx+c=0$ .

In this case, $a=5, b= -11,$ and $c=4$ .

We can factor $1/a + 1/b$ to become $(a+b)/ab$. We can plug our values for a, b, and c in for the sum and product of the roots, giving us the answer of $11/4$ . We don't need to solve for the roots.

Therefore our answer is 11/4. 

I hope this helped.

Use Vieta's formulas.

sum of roots = -b/a

product of roots = c/a

then do some manipulation, don't be lazy