Calculate the discriminant (D = b² - 4ac) to determine the nature of a quadratic's roots.
Quadratic Coefficients
Symbolic Form
ax² + bx + c = 0
(1)x² + (-5)x + (6) = 0
Root Analysis
1
Discriminant (D)
Nature of RootsTwo Distinct Real Roots
Number of Real Roots2
SignPositive
The calculation result implies the quadratic equation has two distinct real roots.
About this calculator
What is the Discriminant?
In algebra, the discriminant of a quadratic equation ax² + bx + c = 0 is the part of the quadratic formula under the square root: b² - 4ac. Its value determines whether the equation has real or complex roots and how many unique solutions exist.
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Pro Tips
If D > 0, there are 2 distinct real roots.
If D = 0, there is exactly 1 real root (a double root).
If D < 0, there are 2 complex (imaginary) roots.
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Fun Facts
"If D is a perfect square and a, b, c are integers, the roots are rational."
"Visually, D > 0 means the parabola crosses the x-axis twice."
"The 'discriminant' tells you if a quadratic can be factored over the real numbers."
