If both x-2 and 2 x-1 are the factors of a x2-5 x-b- show that a- b-0

If (x+2) and (2x 1) are factors, then (x+2)(2x 1)=0 = gt; 2x² x+4x 2=0 = gt; 2x²+3x 2=0 But our obtained equation is not equal to your given equation. So I ...

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Byju's Answer

Standard IX

Mathematics

Factorisation of a Polynomial

If both x+2 a...

Question

If both (x+2) and (2x-1) are the factors of ax² + 5x +b, show that a- b=0

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Solution

If (x+2) and (2x-1) are factors,
then (x+2)(2x-1)=0
=> 2x²-x+4x-2=0
=> 2x²+3x-2=0
But our obtained equation is not equal to your given equation. So I think there is a mistake in your question. The factors would be (x-2) and (2x-1). If so,
If (x-2) and (2x-1) are factors, then polynomial will be
(x-2)(2x-1)=0
⇒2x² -x -4x +2=0
⇒2x²-5x +2 =0
Comparing the obtained equation with given expression,
-(ax²+5x+b)=2x²-5x+2
Hence, a = -2 and b = -2
so, a-b = 0

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