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