Question

If (x-3) and x-1/3 are both factors of ax 2 +5x+b , show that a=b

Answer 1

first multiply (x-3) and (x-1/3)
hence, x^2-10/3x+1 now compare both equations
a/1=+5/-10/3=b/1
a=b=-3/2

Answer 2

Answer:

Factor = (x -3)

x=3

Put values:-

a(3)² + 5(3) + b = 0

a(9) + 15 + b = 0

9a + 15 + b = 0

9a + b = -15 -----》(1)

Factor = (x-1/3)

x = 1/3

Put values:-

a(1/3)² + 5(1/3) + b = 0

a(1/9) + 5/3 + b = 0

a/9 + b = -5/3

a+9b/9 = -5/3

a + 9b = -5/3 × 9

a + 9b = -5 × 3

a + 9b = -15 --------》(2)

Solving equation (1) and (2)

9a + b = a + 9b

9a - a = 9b - b

8a = 8b

Hence a = b is showed here.