Given roots are: x = 2/3 and x = -3
and quadratic equation ax2 + 7x + b = 0
Since x = 2/3 and x = -3 are roots of the above quadratic equation
Hence, will satisfy the given equation.
Step 1: At x = 2/3
a(2/3)2 + 7(2/3) + b=0
4/9 a + 14/3 + b = 0
4a + 42 + 9b = 0 ………….equation (1)
Step 2: At x = –3
a(-3)2 + 7(-3)+b=0
9a – 21 + b = 0 ………….equation (2)
Step 3: Solving equation (1) and equation (2), we get
a = 3, b = –6