Solutions Using the Discriminant
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Key Questions

Answer:
#Delta=b^24ac# for a quadratic#ax^2+bx+c=0# Explanation:
The discriminant indicated normally by
#Delta# , is a part of the quadratic formula used to solve second degree equations.
Given a second degree equation in the general form:
#ax^2+bx+c=0#
the discriminant is:
#Delta=b^24ac# The discriminant can be used to characterize the solutions of the equation as:
1)#Delta>0# two separate real solutions;
2)#Delta=0# two coincident real solutions (or one repeated root);
3)#Delta<0# no real solutions.For example:
#x^2x2=0#
Where:#a=1# ,#b=1# and#c=2#
So:
#Delta=b^24ac=1+4*2=9>0# , giving#2# real distinct solutions.The discriminant can also come in handy when attempting to factorize quadratics. If
#Delta# is a square number, then the quadratic will factorize, (since the square root in the quadratic formula will be rational). If it is not a square number, then the quadratic will not factorize. This can save you spending ages trying to factorize when it won't work. Instead, solve by completing the square or using the formula.I hope that helps!

The quadratic formula states:
For
#ax^2 + bx + c = 0# , the values of#x# which are the solutions to the equation are given by:#x = (b + sqrt(b^2  4ac))/(2a)# The discriminate is the portion of the quadratic equation within the radical:
#color(blue)(b)^2  4color(red)(a)color(green)(c)# If the discriminate is:
 Positive, you will get two real solutions
 Zero you get just ONE solution
 Negative you get complex solutions 
Answer:
To determine how many roots are there in a quadratic equation.
Explanation:
There are 4 natures
#b^24ac>0# and is a perfect square ># 2 rational roots#b^24ac>0# and is not a perfect square#># 2 irrational root
#b^24ac=0 ># 1 root
#b^24ac <0# No root
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Quadratic Equations and Functions

1Quadratic Functions and Their Graphs

2Vertical Shifts of Quadratic Functions

3Use Graphs to Solve Quadratic Equations

4Use Square Roots to Solve Quadratic Equations

5Completing the Square

6Vertex Form of a Quadratic Equation

7Quadratic Formula

8Comparing Methods for Solving Quadratics

9Solutions Using the Discriminant

10Linear, Exponential, and Quadratic Models

11Applications of Function Models