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Yes. If the discriminant (of a quadratic equation) is...
- Positive: There are two real roots.
- Zero: There is a single "double" root. ("Double" means that if you factor, you will have a repeated factor.)
- Negative: There are two complex roots (and no real roots).
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What are 3 outcomes for the discriminant?
If the discriminant of a quadratic equation is zero then it has equal roots. If the discriminant is greater than zero then there are two different roots. If the discriminant is less than zero then there are no real roots.
If the discriminant is negative the equation has?
No real roots but the roots are a pair of complex conjugates.
What is the discriminant of x2 3x 4?
The discriminant of x2+3x+4 is -7 therfore it has no real roots.
How do you find the discriminant and number of real solutions to a quadratic equation?
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula Δ = b^2 - 4ac. The discriminant helps determine the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one real root (a repeated root); and if Δ < 0, there are no real roots (two complex conjugate roots). The number of real solutions is directly related to the discriminant's value.
What use the discriminant to determine the nature of the roots of x2 plus 2x plus 5 equals 0?
No real roots
