If (x-3) and (x-1/3) are both factors of ax(square)+5x+b, show that a=b.
qais:
That will be -5x not +5x
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If (x-3) and (x-1/3) are factors, then polynomial will be
(x-3)(x-1/3)=0
⇒x² -x/3 -3x +1=0
⇒x²-10x/3 +1 =0
⇒3x²-10x +3 =0
⇒(3/2)x² -5x +(3/2) = 0
comparing with the actual equation,
Hence, a = 3/2 and b = 3/2
so, a=b
(x-3)(x-1/3)=0
⇒x² -x/3 -3x +1=0
⇒x²-10x/3 +1 =0
⇒3x²-10x +3 =0
⇒(3/2)x² -5x +(3/2) = 0
comparing with the actual equation,
Hence, a = 3/2 and b = 3/2
so, a=b
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