Question

Find the number of real zeros of P(x) = (x - 2)^2+3:
(1) 1
(2) 0
(3) 2
(4) None of these
Please answer with solution​

Answer 1

Answer:

option (2). 0

Step-by-step explanation:

$p(x) = {x}^{2} - 4x + 4 + 3 \\ \\ = {x}^{2} - 4x + 7 \\ \\ d = {b}^{2} - 4ac \\ \\ = {( - 4)}^{2} - 4(1)(7) \\ \\ = 16 - 28 \\ \\ = - 12 < 0 \\ \: \: \: \: \: \: \\ \\ \\ d < 0\\ \\ option \: (2) \: \: 0 \: \: \: \: \: \: \: \: is \: \: \: correct.$