Question

Is polynomial y4 + 4y2 + 5 have zeroes or not?​

Answer 1

Answer:

The polynomial y4 + 4y2 + 5 has no zero(s) because the roots are not real. Since the first term has a degree of 4, it cannot be possible because it is not in the form of a quadratic equation, hence no zeroes.

Answer 2

Answer:

No, the polynomial equation $y^{4}$ + 4y² + 5 does not have any zeroes.

Step-by-step explanation:

Given :- The given polynomial equation is  $y^{4}$ + 4y² + 5 = 0.

To Find :- If the polynomial equation $y^{4}$ + 4y² + 5 = 0 have zeroes or not.

Solution :-

A polynomial equation is an equation formed with sum of variables, non-negative integers, exponents, and coefficients together.

The given polynomial equation $y^{4}$ + 4y² + 5 is of degree 4.

We know that,   (a +b)² = a² + b² + 2ab

$y^{4}$ + 4y² + 5 = 0

⇒  $y^{4}$ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

The expression (y² + 2)² + 1 will not be zero for any value of y since the 1st term is a square.

Therefore, the polynomial equation  $y^{4}$ + 4y² + 5 will not have any real roots.

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