Question

the number of zeroes that polynomial f(x)=(x+2)²+6 can have is
a) 0
b) 1
c) 2
d) 3​

Answer 1

Answer:

a) 0

Step-by-step explanation:

Given polynomial: (x + 2)² + 6

Used identity: (a + b)² = a² + b² + 2ab

→ x² + 4 + 2(x)(2) + 6

→ x² + 4 + 4x + 6

→ x² + 4x + 10

On comparing x² + 4x + 10 with ax² + bx + c. We have a = 1, b = 4 and c = 10.

Now,

D = b² - 4ac

Substitute the values,

D = (4)² - 4(1)(10)

D = 16 - 40

D = -24

D < 0

Therefore, the number of zeros that polynomial f(x)=(x+2)²+6 can have is 0.