Q.>if x= 2/3 and x= -3 are the roots of the equation ax2 +7x+b=0, find the value of a and b.
Given, and x = – 3 are the roots of the quadratic equation .
...(1)
Putting in equation (1), we get
Putting x = – 3 in equation (1), we get
⇒ 9a – 21 + b = 0
⇒ 9a + b = 21
⇒ b = 21 – 9a ...(3)
Solving (2) and (3), we get
4a + 9 ( 21 – 9a) = – 42
⇒ 4a + 189 – 81a = – 42
⇒ –77a = – 42 – 189 = – 231
⇒ a = 3
Putting the value of a in (3), we get
b = 21 – 9 × 3 = 21 – 27 = – 6
Thus, the value of a and b is 3 and – 6 respectively.