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Question
If (x-1) and (x-1/3)are both the factors of ax2+ 5x + b , then show that a=b.
If (x-1) and (x-1/3)are both the factors of ax2+ 5x + b , then show that a=b.
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Solution
Ax²+5x+b = 0
We get the exact quadratic equation when we multiply the both factors.
So
(x–3)(x–⅓) = x²–(3+⅓)x+1
= x²–(10/3)x+1
x²–(10/3)x+1 = 0
Sum of roots = –5/a = 10/3
a = –5×(3/10) = –3/2
Product of roots = b/a = 1
a = b
We get the exact quadratic equation when we multiply the both factors.
So
(x–3)(x–⅓) = x²–(3+⅓)x+1
= x²–(10/3)x+1
x²–(10/3)x+1 = 0
Sum of roots = –5/a = 10/3
a = –5×(3/10) = –3/2
Product of roots = b/a = 1
a = b
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