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Determine whether the given quadratic equation …

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Determine whether the given quadratic equation has real roots or not. x 2 - 2x + 1 = 0.

Posted by Ok Wahsi 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

We have been given, x² - 2x + 1 = 0

Now we also know that for an equation ax² + bx + c = 0, the discriminant is given by the following equation:

D = b² - 4ac

Now, according to the equation given to us, we have,a = 1, b = -2 and c = 1.

Therefore, the discriminant is given as,

D = (-2)² - 4(1)(1)

= 4 - 4

= 0

Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation satisfies this condition, hence it has real and equal roots.

Now, the roots of an equation is given by the following equation,

x=-b± underroot D / 2a

Therefore, the roots of the equation are given as follows,

x=-(-2)±0 / 2(1)

=2 / 2

= 1

Therefore, the roots of the equation are real and equal and its value is 1.

0Thank You

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CBSE > Class 10 > Mathematics