Question

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

Answer 1

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→ Here is ur questions answer:


⇒ Given, f(x) = x power 4 + 4x2 + 6
               = (x2) power 2 + 4x2 + 6

⇒ Put x power 2 = a

∴  x power 4 + 4x2 + 6 = (x2) power 2 + 4x power 2 + 6
                             = a power 2 + 4a + 6

⇒ To find the zero of the above polynomial, we take a power 2 + 4a + 6 = 0

⇒ The above equation does not have a real root

⇒ Hence there is no zero for this given polynomial.

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Answer 2

let x^2 be a

a^2 + 4a +6

discriminant= b^2 - 4 a × c

d=4^2 - 4 × 1 ×6

d=16- 24

d=-8

If discriminant is negative there is no real root

HOPE THIS IS RIGHT