the author discusses how to know the number and types of solutions to a

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quadratic equation using the discrimi? the author discusses how to know the number and types of solutions to a quadratic equation using the discriminant.

What is the discriminant?

How is it found?

After reviewing the quadratic formula, why does the sign of the discriminant determine the number of real or imaginary solutions? (Hint: a number is imaginary if it contains the principal square root of a negative number.)

Can you tell by analyzing the discriminant if the quadratic equation could be solved by factoring?

Use examples as appropriate to illustrate your responses.
 
The discriminant in a quadratic function of the form:
ax^2 + bx + c = 0
is classified as: b^2 - 4ac
By substituting the values for a, b, and c from the quadratic given, you can find the value of the discriminant.
If the value of the discriminant is more than 0, then there are 2 distinct real roots.
If the value of the discriminant is equal to 0, then there is only 1 real distinct root.
If the value of the discriminant is less than 0, there are no real roots, or 2 imaginary complex conjugate roots.
Conjugate roots are of the form: a + bi and a - bi.
Distinct means that the two value are different in some way.

Hope that helped.
 
The discriminant is the part of the Quad Form that is under the radical (sq rt).

It is found by substituting the values for A, B and C into the b^2 -4ac part of the QF.


If the discriminant is negative that means the types of roots are complex numbers of the form a + bi or a - bi

Complex numbers must occur in pairs, if the values of a, b, and c are real numbers.

If the discriminant is zero there is one real root with what is called a duplicity of 2 (2 roots with the same value)

If the discriminant is positive there are 2 real roots


If the discriminant is a perfect square, it can be factored. Sometimes, if you are familiar with the rules of factoring trinomials, you may be able to factor the quad eq'n even though the discriminant is not a perfect square. ( But, usually it is much more difficult.)

Good Luck.
 
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