Describe the nature of the roots of this equation 2x^2-x+1=0

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Mathematics

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28 January, 04:53

Describe the nature of the roots of this equation 2x^2-x+1=0

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Lorenzo Pruitt · Answer 1

X^2 - 2x + 1 = (x - 1) ^2.

So, x^2 - 2x + 1 = 0

==> (x - 1) ^2 = 0.

By the Zero-Product Property, x = 1 is the only solution. However, since the x - 1 factor is squared, 1 is a zero of multiplicity 2 and is thus a double-root.

Meaning, the answer is D.