Question

16. Show that the polynomial f(x) = x4 + 4x + 6 has no zero.​

Answer 1

Answer:Given, f(x) = x4 + 4x2 + 6 We can rewrite the given equation as ⇒ f(x)= (x2)2 + 4x2 + 6 Let x2 = a ⇒ f(x) = a2 + 4a + 6 If the discriminant of the equation < 0 then the given polynomial has no zeros.Discriminant = b2- 4ac = 42 - 4(1)(6) =16 - 24 = - 8 < 0Therefore, there is no zero for given polynomial

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