Question

1. Show that the polynomial f(x) = x^4+4x^2 +6 has no zero.​

Answer 1

Step-by-step explanation:

$f(x) = {x}^{4} + 4 {x}^{2} + 6 \\ let \: us \: substitute \: x = 0 \: in \: f(x) \\ \implies f(0) = {0}^{4} + 4 \times {0}^{2} + 6 \\ \implies f(0) = 0 + 0 + 6 \\ \implies f(0) =6 \\ \because \: at \: x = 0 \: f(x) \neq \: 0 \\ \therefore \: Polynomial \: f(x) \: has \: no \: zero.$