If the two zeroes of the polynomial f(x) = x3 – 6x2 + mx + n are 2 +

1.	If the two zeroes of the polynomial f(x) = x3 – 6x2 + mx + n are 2 + root5 and 2 - root 5, then find third zero and values of m and n.
Answer» Step-by-step explanation: X=1 f(1)=1^3-6(1)^2+m×1-N=0 =1-6+m-n=0 =-5+m-n=0 =m=n+5 ... (1) If f(x) =x^3-6x^2+mx-n is EXACTLY divisible by x-2 So x-2=0 x=2 f(2)=2^3-6(2)^2+m×2-n=0 =8-24+2m-n=0 =-16+2m-n=0 =2m-n=16 ... (2) From eq 1&2 2(n+5)-n=16[m=n+5] 2n+10-n=16 n=16-10 n=6 Putting the value of n in eq 1 m=6+5 m=11

If the two zeroes of the polynomial f(x) = x3 – 6x2 + mx + n are 2 + root5 and 2 - root 5, then find third zero and values of m and n.

Answer»

Step-by-step explanation:

X=1

f(1)=1^3-6(1)^2+m×1-N=0

=1-6+m-n=0

=-5+m-n=0

=m=n+5 ... (1)

If f(x) =x^3-6x^2+mx-n is EXACTLY divisible by x-2

So x-2=0

x=2

f(2)=2^3-6(2)^2+m×2-n=0

=8-24+2m-n=0

=-16+2m-n=0

=2m-n=16 ... (2)

From eq 1&2

2(n+5)-n=16[m=n+5]

2n+10-n=16

n=16-10

n=6

Putting the value of n in eq 1

m=6+5

m=11