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If a quadratic equation is ax2+bx+c
then we can learn something about the roots withoutcompletely solving the quadratic formula.
The discriminant is b2-4ac. You may recognize this as part of the quadratic formula.
If the value is a non-zero perfect square, there are 2 rational roots
If the value is an imperfect square, there are 2 irrational roots
If the value is zero, there is 1 rational root (parabola vertex is on the x-axis)
If the value is negative, there are imaginary roots (no intersection with x-axis)
The discriminant, therefore, tells us the nature of the roots.
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How do you tell if a discriminant is positive negative or zero?
With the standard notation, If b2 < 4ac then the discriminant is negative If b2 = 4ac then the discriminant is zero If b2 > 4ac then the discriminant is positive
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.
What is the discriminant of the polynomial below?
That depends on the values of the polynomial but in general:- If the discriminant is greater than zero it has 2 solutions If the discriminant is equal to zero then it has 2 equal solutions If the discriminant is less than zero it has no solutions
What is the discriminant of 2x2 plus 23x plus 63 equals 0?
The discriminant is 25.
If the discriminant of an equation is 0?
If the discriminant of a quadratic equation is zero then it has two identical roots.
