Question

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

Answer 1

Answer:

as both are the factors of the equation

therefore x-2=0. and x-1/2 =0

X=2,1/2

put in equation

n(2)^2-5(2)+m=0

4n-10+m=0

4n+m=10. (a)

n(1/2)^2-5(1/2)+m=0

n/4-5/2+m=0

n+4m/4= 5/2. (b)

Subtract equation a and b

( 4n-n)+(m-4m)=10-10

3n-3m=0

3n=3m

n=m

keep in any equation

say a

4m+m=10

5m=10

m=2

answer=n=m=2