standard form of a quadratic equation
ax² + bx + c = 0
The standard form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are constants and x is the variable. The quadratic equation can be solved using the quadratic formula:
x = [-b ± √(b^2 – 4ac)] / 2a
This formula provides two solutions for x, which are the roots of the quadratic equation. The value inside the square root is called the discriminant and determines how many real solutions the equation has:
– If the discriminant is positive (b^2 – 4ac > 0), then the equation has two distinct real roots.
– If the discriminant is zero (b^2 – 4ac = 0), then the equation has one real root (which is also called a double root).
– If the discriminant is negative (b^2 – 4ac < 0), then the equation has two complex roots (which are conjugate pairs).
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