Question

If x=2/3 and x=-3 are the roots of equipment ax2+7x +b =0 find the values of a and b

Answer 1

As coefficients a'=a ,b'=7, c'=b of Quadratic.

Roots are α=2/3 and β=-3

sum of roots =α+ β=-b'/a'
2/3 + (-3) =-7/a
(2-9)/3 = -7/a
-7/3=-7/a
a=3

product of roots=αβ=(2/3)*(-3)=>-2/3=c'/a'
=> -2/3=b/a
=> -2a=3b
=> -2*3=3b [as a=3]
=> b=-2

Hence a=3 and b=-2