Please answer fast
1) Show that the polynomial x2+4x+5 has no zero .
2) For what value of m is x3- 2mx2 + 16 divisible by x+2 ?
1)
Given, polynomial = x2 + 4x+ 5
In order to prove that it has no zeros, we have to show that its discriminant (D) < 0.
So, D = b2-4ac = (4)2 - 4 × 1 × 5 = 16 - 20 = -4 < 0
Hence, the given polynomial doesn't have rational zeros.
2)
Let the given polynomial be f(x) = x3- 2mx2 + 16.
It is given that f(x) is divisible by x+2, i.e., x = -2 is a factor of f(x).
So, f(-2) = 0
⇒ (-2)3- 2m(-2)2 + 16 = 0
⇒ -8- 8m + 16 = 0
⇒ - 8m + 8 = 0
⇒ - 8m = - 8
⇒ m = 1
Hence, for m = 1, f(x) is divisible by (x+2).