Q. 123.7( 31 Votes )

If x-2 and x – 1/2 both are the factors of the polynomial nx2 – 5x + m, then show that m= n=2

Answer :

Put x = 2 in the given polynomial:

n× 4 – 5× 2 + m = 0


4n + m = 10 ……………………………. (i)


Put x = 1/2 in the given polynomial


n × 1/4 - 5 × 1/2 + m = 0


n + 4m – 10 = 0


n + 4m = 10 ……………………………….. (ii)


Since the RHS of both the equations is same,


4n + m = n + 4m


3n = 3m


n = m


Put n = m in the equation (i)


4m + m = 10


5m = 10


m = 2 = n


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