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Here are a few recommended readings before getting started with this lesson.
A quadratic equation is a polynomial equation of degree 2. There is a special name for quadratic equations whose linear coefficient b is 0. These equations can be written in the form ax2+c=0 and have their own characteristics.
If the linear coefficient b of a quadratic equation is 0, the equation is called a simple quadratic equation and can be written in the following form.
ax2+c=0
This type of equation can be solved using inverse operations. Once x2 is isolated, the equation can be written as x2=d, where d=-ac. The value of d gives the number of solutions the equation has.
The cases d>0, d=0, and d<0 will be discussed one at a time.
Because the square of any real number is always greater than or equal to 0, if d<0 the equation x2=d has no real solutions.
Without solving the simple quadratic equations, determine the number of real solutions.
Apart from determining the number of real solutions of a simple quadratic equation, most of the times it is important to calculate those solutions.
LHS=RHS
a2=±a
Calculate root
State solutions
Ali and Heichi are enjoying a ski vacation.
Heichi told Ali that he would pay for an extra hotel night if Ali could solve the following quadratic equation.Start by isolating x2.
LHS=RHS
a2=±a
ba=ba
Calculate root
State solutions
Start by isolating x2.
LHS=RHS
a2=±a
State solutions
(I), (II): Use a calculator
(I), (II): \RoundSigDig{3}
Solve the following simple quadratic equations by taking square roots. If necessary, round the solutions to two decimal places.
Jordan is representing North High School in an algebra competition.
She has been challenged with a quadratic equation that is a bit more complicated than a simple quadratic equation.Start by isolating (x−5)2.
Equation | Rewrite |
---|---|
-x2+4=0 | -1(x−0)2+4=0 |
3x2−6x+5=0 | 3(x−1)2+2=0 |
5x2=3x+1 | 5(x−103)2+(-2029)=0 |
4x2+4x=-2 | 4(x−(-21))2+1=0 |
4x2+4x=-2 | 4(x−(-21))2+1=0 |
10x2+160=80x | 10(x−4)2+0=0 |