Question

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

Answer 1

if they are factor then the value of the polynomial at 2 and 1/2 would be zero.
so putting the value ,we get
4n-10+m=0. equ 1
n/4-5/2+m=0 equ 2
on solving them we get n=m=2

Answer 2

Answer:

m = n = 2

Step-by-step explanation:

If (x-2) and (x - 1/2) are the factors of the polynomial than the value of polynomial at x = 2 and x = 1/2 would be 0.

If we put x = 2 in $nx^2 - 5x + m = 0$

than,

$n \times 2^2 - 5 \times 2 + m = 0$

4n - 10 + m = 0   -------- equation 1

If we put x = 1/2 in $nx^2 - 5x + m = 0$

than,

$n \times [\frac {1} {2}]^2 - 5 \times \frac {1} {2} + m = 0$

$\frac {n} {4} - \frac {5} {2} + m = 0$

n - 10 + 4m = 0   -------- equation 2

Now, multiply by 4 in equation 1 and than subtract from equation 2

n - 10 + 4m - (16n - 40 + 4m) =  0

n - 10 + 4m - 16n + 40 -4m = 0

-15n + 30 = 0

15n = 30

n = $\frac {30}{15}$

n = 2

Now, put n = 2 in equation 1

4 × 2 - 10 + m = 0

8 - 10 + m = 0

-2 + m = 0

m =2

So, here is the value of m = n =2

Hence Proved