Question

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

Answer 1

Given that (x - 3) and ( x - 1/3) are factors,

Then, x = 3 or 1/3

Taking x = 3


ax² + 5x + b = 0

a(3)² + 5(3) + b = 0

9a + 15 + b = 0

9a + b = -15

b = -15 - 9a ------1equation




××××××××××××××××××


Taking x = 1/3

ax² + 5x + b = 0

a(1/3)² + 5(1/3) + b = 0

a/9 + 5/3 + b = 0

a + 9b = -15 ------2equation

×××××××××××××××××

Putting the value of b from 1equation,

a - 135 - 81a = -15

-80a = -15 + 135

-80a = 120

a = -3/2


Putting the value of a in 1equation,

b = -15 - 9(-3/2)
b = -15 + 27/2
b = (-30 + 27)/2
b = -3/2

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Hence, -3/2 = -3/2

a = b


I hope this will help you

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