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Show that the polynomial f(x) = …

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Show that the polynomial f(x) = x⁴+4x²+6 has no zeros

Posted by Cute Boy 1 year, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Sourav Singh 1 year, 6 months ago

Let x^2 =t then the given equation reduces to t^2+4t+6=0 D=b^2 −4ac D=(4)^2−4(6)(1) D=16−24=−8 D<0 Discriminant is less than zero,so the given equation has imaginary roots. As all the 3 terms in this polynomial are all positive, this polynomial can never become zero for real values of x. Hence, the given polynomial has no real

Parv Jain 1 year, 6 months ago

Let x^2 =t then the given equation reduces to t^2+4t+6=0 D=b^2 −4ac D=(4)^2−4(6)(1) D=16−24=−8 D<0 Discriminant is less than zero,so the given equation has imaginary roots. As all the 3 terms in this polynomial are all positive, this polynomial can never become zero for real values of x. Hence, the given polynomial has no real zeros.

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