Properties
of roots of a quadratic equation. Viete’s theorem
Roots of quadratic equation. Discriminant. Viete's
theorem.
The formula
shows, that the three cases are
possible:
1) b
2 – 4 a
c > 0 , then
two roots are different real numbers;
2) b
2 – 4 a
c = 0 , then two
roots are equal real numbers;
3) b
2 – 4 a
c < 0 , then
two roots are imaginary numbers.
The expression b 2 –
4 a c , value of which permits to differ
these three cases, is called a discriminant of a
quadratic equation and marked as D.
Viete’s theorem. A sum of roots of reduced quadratic
equation
x2+ px + q = 0 is equal to coefficient at the first power
of unknown, taken with a back sign,
i.e.
x1 + x2 = – p ,
and a product of the roots is equal to a
free term, i.e.
x1
· x2 = q .
To prove Viete’s theorem, use
the formula, by which roots of reduced quadratic equation are
calculated.
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