The roots of 7x^2 + x - 5 = 0 are a and b. Compute 1/a + 1/b.
Use Vieta's calcs
ab = -5/7
a+b = -1/7
1/a + 1/b multiply first term by b/b second term by a/a
b/ab + a/ab = ( b + a )/ab sub in the red values above
1/a + 1/b = (-1/7) / (-5/7 ) = 1/5
+37157 
