Find quadratic equation using the quadratic formula, Mathematics

Find quadratic equation using the Quadratic Formula:

Solve the subsequent quadratic equation using the Quadratic Formula.

4x2 + 2 = x2 - 7x:

Solution:

Step 1. Write the equation in general forms.

4x2 + 2 = x2 -7x

3x2 + 7x + 2 = 0

a= +3, b = +7, c = +2

1029_Find quadratic equation using the Quadratic Formula.png

Step 2.

x = (6 ± √20)/2

x = 3 ± 1/2√20

2446_Quadratic Formula2.png

x = 3 ± √5

x = 3 + √5, 3 - √5

x = 3 + 2.236, 3 -2.236

x = 5.236, 0.746

Step 3. Check the roots.

2x2 + 4 = 6x +x2

2(3 + √5)2 +4 = 6(3 + √5) + (3+√5)2

2(9 + 6√5 + 5) + 4 = 18 +6√5 + 9 + 6√5 + 5

18 + 12√5 + 10 + 4 = 18 + 12√5 + 9 +5

32+ 12√5 = 32 + 12√5

And,

2x2 + 4 = 6x + x2

2(3-√5)2 + 4 = 6(3- √5) + (3 - √5)2

2(9-6√5 + 5) + 4 = 18-6√5 + 9 -6√5 + 5

18 - 12√5 + 10 + 4 = 18 - 12√5 + 9 + 5

32- 12√5 = 32 - 12√5

Thus, the roots check.

The Quadratic Formula can be used to search the roots of any quadratic equation.   For a pure quadratic equation in that the numerical coefficient b equals zero, the Quadratic Formula (2-8) decreased to the formula given as Equation 9.

1297_Find quadratic equation using the Quadratic Formula2.png                                                                   

For b = 0, this decreases to the subsequent.

1284_Find quadratic equation using the Quadratic Formula3.png                                                                           

Posted Date: 2/9/2013 3:13:43 AM | Location : United States







Related Discussions:- Find quadratic equation using the quadratic formula, Assignment Help, Ask Question on Find quadratic equation using the quadratic formula, Get Answer, Expert's Help, Find quadratic equation using the quadratic formula Discussions

Write discussion on Find quadratic equation using the quadratic formula
Your posts are moderated
Related Questions
Let 0 ! V1 !    ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.

How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries?


The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field

How many arrangements can be made from the letters of the word " VENUS " such that the order of the vowels remains the same?

Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt? Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part

Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is

Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves.  Note also that we said "enclosed by" in place of "under" as we usually have

Definition of Relation A relation is a set of ordered pairs. It seems like an odd definition however we'll require it for the definition of a function though, before actuall

simplify mn+mp+nq+pq /n+p