Complex solutions of quadratic equations, Algebra

Assignment Help:

These are the only possibilities for solving quadratic equations in standard form.  However Note that if we begin with rational expression in the equation we might get different solution sets since we might have to ignore one of the possible solutions thus we don't get division by zero errors.

Now, it turns out that all we have to do is look at the quadratic equation (in standard form of course) to find out which of the three cases that we'll get.  In order to see how this works let's begin by recalling the quadratic formula.

1499_Complex solutions of quadratic equations.png

The quantity b2 - 4ac in the quadratic formula is called the discriminant.   It is the value of the discriminant which will determine which solution set we will get.  Let's go through the cases one at a time.

1.   Two real distinct solutions. We will obtain this solution set if b2 - 4ac >0.  In this case we will be taking square root of positive number & hence the square root will be a real number.  Thus the numerator in the quadratic formula will be   -b plus or minus a real number. It means that the numerator will be two different real numbers.  Dividing either one through 2a won't vary the fact that they are real, nor will it vary the fact that they are distinct.

2.   A double root.  We will obtain this solution set if b2 - 4ac = 0 .  Here we will be taking the square root of zero that is zero.  Though, it means that the "plus or minus" part of the numerator will be zero and thus the numerator in the quadratic formula will be -b.  In other terms, we will get a single real number out of the quadratic formula that is what we get while we get a double root.

3.   Two complex solutions. We will obtain this solution set if b2 - 4ac < 0.  If the discriminant is -ve we will be taking the square root of negative numbers in the quadratic formula that means that we will obtain complex solutions.  Also, we will obtain two since they have "plus or minus" in front of the square root.

Hence, let's summarize up the results here.

1.   If b2 - 4ac>0 then we will obtain two real solutions to the quadratic equation.

2.   If b2 - 4ac = 0 then we will obtain a double root to the quadratic equation.

3.   If b2 - 4ac <0

then we will obtain two complex solutions to the quadratic equation.


Related Discussions:- Complex solutions of quadratic equations

Hcf, how to find hcf easily

how to find hcf easily

Evaluating radical expressions, Express the answer as an integer, simplifie...

Express the answer as an integer, simplified fraction, or a decimal rounded to two decimal places.

Formula, using the formula for the difference between two squares,factor th...

using the formula for the difference between two squares,factor the following : 5-x

Tests for symmetry, We've some rather simply tests for each of the distinct...

We've some rather simply tests for each of the distinct types of symmetry. 1. A graph will have symmetry around the x-axis if we get an equal equation while all the y's are repl

Write & Solve Equations, Lisa and Judy read mystery novels. Judy has read ...

Lisa and Judy read mystery novels. Judy has read three fewer than five times as many as Lisa. Equation: J=5L-3 Lisa: Judy:

Word problem with three variables, Three students were participating in a s...

Three students were participating in a school''s fundraiser. The first student sold 2 candy bars, 7 pies, and 3 cookie dough. The second student sold 10 candy bars, 2 pies, and 2 c

Solving problem using polynomial inequalities, Example Solve 3x 2 - 2 x -...

Example Solve 3x 2 - 2 x -11 = 0. Solution In this case the polynomial doesn't factor thus we can't do that step.  Though, still we do have to know where the polynomial i

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd