Q. 155.0( 2 Votes )

If (x – 3) and both are factors of ax2 + 5x + b, then show that a = b.

Answer :

Let p(x) = ax2 + 5x + b


As (x – 3) and are factors of p(x) hence each will divide p(x) leaving remainder as 0


Let us use the remainder theorem which states that if (x – a) divides a quadratic polynomial p(x) then p(a) = 0


p(3) = 0


Substituting x = 3


a(3)2 + 5(3) + b = 0


9a + 15 + b = 0


b = – 9a – 15 …(ii)


And also


Substituting




Multiplying throughout by 9


a + 15 + 9b = 0


–9b = a + 15 …(i)


Add (i) and (ii)


b – 9b = – 9a – 15 + a + 15


–8b = –8a


a = b


Hence proved


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