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subject: Quadratic Equations Problems [print this page]

Introduction to Quadratic equation:
Introduction to Quadratic equation:

The equations that are having the highest degree term x^2 or second degree are called as Quadratic Equations. The standard form of the quadratic equation is, ax^2+bx+c=0

Based on the quadratic equations we can ask three questions,

1. Solve the quadratic Equations

2. Find the Factors of the quadratic equations

3. Find the zero"s of the quadratic equations

We can solve the quadratic equations by using two methods,

1. Solve by Factoring

2. Solve by using Quadratic formula

Quadratic Equations Problems: solve by Factoring

Using factoring method, we can solve the problems of quadratic equations. Some of the quadratic equations can be rewritten as factor format. To find the factors we use the diamond box method.

Consider the following example problem,

x^2+3x+2=0

By using the diamond box method, we can split,

2=1*2 (product)

3= 1+2 (sum)

So we can write the above equation as,

x^2+ (1x+2x) +2=0

(x^2+1x)+ (2x+2)=0

x(x+1) +2(x+1)=0

(x+1)(x+2)=0

x+1=0 and x+2=0

x=-1 and x=-2

So the solution is -1,-2.The quadratic Equations are always having two solutions.

Practice Problems:

Solve the following problems on quadratic equations by factoring method :

1. Solve the quadratic equation by Factoring, x^2-5x-6=0

2. Solve by factoring, x^2+x-2=0

3. Solve the quadratic equation by Factoring, x^2+2x+1=0

4. Solve the quadratic equation by Factoring, 3x^2-6x+3=0

5. Solve the quadratic equation by Factoring, -x^2+5x+6=0

6. Solve the quadratic equation by Factoring, 5x^2-9x-2=0

7. Solve the quadratic equation by Factoring, x^2-3=2x

8. Solve the quadratic equation by Factoring, x(x+5) =0

9. Solve the quadratic equation by Factoring, 9x^2-6x+1=0

10. Solve the quadratic equation by Factoring, 8x^2-18x-5=0

Answer key:

1.(6,-1)

2.(1,-2)

3.(-1,-1)

4.(1,1)

5.(-1,6)

6.(2,-0.2)

7.(3,-1)

8.(0,-5)

9.(0.33,0.33)

10.(2.5,-0.25)

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Quadratic Equations Problems: solve by Using Quadratic Formula:

We can also solve the problems on quadratic equations using quadratic formula. Suppose if we can"t able to solve the quadratic equation by using factoring method, we can use the quadratic formula to find the solution,

The quadratic formula is,

X= (-bv (b^2-4ac))/2a

For example,

3x^2+5x+10=0

Here a=3, b=5, c=10.Substitute the values in the above formula and we can get the solution x= - 0.833+1.62i and

x=- 0.833-1.62i .

Practice problems:

The sample problems based on solving quadratic equations using quadratic formula are given below:

1. Solve by using quadratic formula 3x^2-2x-4=0

2. Solve by using quadratic formula 5x^2-9x-2=0

3. Solve by using quadratic formula 5x^2-18x-3=0

4. Solve by using quadratic formula x^2-8x-6 =0

5. Solve by using quadratic formula 5x^2-7x-6 =0

Answer Key:

1.(1.535,-0.87)

2.(2,-0.2)

3.(3.76,-0.16)

4.(8.69,-0.69)

5.(2,-0.6)

by: mathqa

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