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Class 10 > Learn Mathematics > Is polynomial y4 + 4y2 + 5 have zeroes or not?
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Is polynomial y4 + 4y2 + 5 have zeroes or not?

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The polynomial y4 + 4y2 + 5 has no zero(s) because the roots are not real.
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Y4+4y2+5=y4+4y2+4 +1 =(y2+2)2+1 The first term being square,it will be equal to zero or greater than zero. Therefore (y2+2)2+1 will not be zero for any value of y. Therefore given polynomial have no zeroes.
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?
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No. Because y^4 & y^2 can never be negative. So atleast those have to be 0 each. So, this polynomial can never be 0.
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Is polynomial y^4+4y^2+5 have zeroes or not
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10 years of teachimg experience in maths, Maths onlie tutor from 6 th to 10

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10 years of teachimg experience in maths, Maths onlie tutor from 6 th to 10

Given, f(x) = x4 + 4x2 + 5 = (x2)2 + 4x2 + 5 Put x2 = a Hence x4 + 4x2 + 5 = (x2)2 + 4x2 + 5 = a2 + 4a + 5 To find the zero of the above polynomial, we take a2 + 4a + 5 = 0 The above equation does not have a real root Hence there is no zero for this given...
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Given, f(x) = x4 + 4x2 + 5

                 = (x2)2 + 4x2 + 5

Put x2 = a

Hence x4 + 4x2 + 5 = (x2)2 + 4x2 + 5

                              = a2 + 4a + 5

To find the zero of the above polynomial, we take a2 + 4a + 5 = 0

The above equation does not have a real root

Hence there is no zero for this given polynomial.

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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.
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Not equal to 0
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