How do you find the discriminant of $x^{2} - 2 x + 1 = 0$ $x^2-2x+1=0$ and use it to determine if the equation has one, two real or two imaginary roots?

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How do you find the discriminant of $x^{2} - 2 x + 1 = 0$ $x^2-2x+1=0$ and use it to determine if the equation has one, two real or two imaginary roots?

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Answer 1 · 2017-05-13T03:31:48

$Delta =0 ->$ equation has a one real solution $x=1$

Explanation:

Consider the general form of the quadratic equation:

$ax^2+bx+c=0$

The discriminant $(Delta)$ is defined as: $b^2-4ac$

Three cases arise:

(i) $Delta >0 ->$ the equation has two distinct real roots
(ii) $Delta <0 ->$ the equation has two complex roots
(iii) $Delta =0 ->$ the equation has one real solution (Strictly, two equal real roots)

In our equation: $x^2-2x+1=0$

$Delta = (-2)^2-4*1*1 = 4-4 =0$

Hence the equation has one real solution.

The equation may be factorised as: $(x-1)(x-1)=0$

Hence the only real solution is $x=1$

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How do you find the discriminant of $x^{2} - 2 x + 1 = 0$ $x^2-2x+1=0$ and use it to determine if the equation has one, two real or two imaginary roots?

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Explanation:

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How do you find the discriminant of x^2-2x+1=0x2−2x+1=0x^2-2x+1=0 and use it to determine if the equation has one, two real or two imaginary roots?

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Explanation:

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How do you find the discriminant of $x^{2} - 2 x + 1 = 0$ $x^2-2x+1=0$ and use it to determine if the equation has one, two real or two imaginary roots?