Welcome to mathhomeworkanswers.org. Start by asking a new question, answering unanswered questions or registering or a free account!
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages geometry problems calculus problems fraction problems math problem trigonometry problems simplifying expressions rounding numbers solve for x order of operations pre algebra problems algebra evaluate the expression slope intercept form please answer this queastion as soon as possible. thank you :) probability factoring please help me to answer this step by step. word problem plz. give this answer as soon as possible statistics problems polynomials solving inequalities how to find y intercept algebra 2 problems logarithmic equations equation of a line solving systems of equations by substitution help sequences and series dividing fractions greatest common factor square roots graphing linear equations geometric shapes 6th grade math long division substitution method solving systems of equations least common multiple factoring polynomials least to greatest http: mathhomeworkanswers.org ask# solving equations with fractions ratio and proportion standard form of an equation dividing decimals function of x help me!! proving trigonometric identities algebra problem trig identity solving equations with variables on both sides precalculus problems ( slope of a line through 2 points help me domain of a function solving systems of equations by elimination algebraic expressions i need help with this college algebra distributive property trinomial factoring solving quadratic equations factors of a number perimeter of a rectangle slope of a line greater than or less than division differentiation fraction word problems 8th grade math limit of a function exponents how to find x intercept equivalent fractions differential equation algebra word problems elimination method algebra 1 hw help asap simplifying fractions area of a triangle 7th grade math inverse function geometry 10th grade geometry . fractions story problems simplify integral area of a circle standard deviation circumference of a circle place value parallel lines systems of equations containing three variables solving triangles width of a rectangle mixed numbers to improper fractions solving linear equations percentages scientific notation problems number of sides of a polygon zeros of a function homework prime factorization area of a rectangle solving systems of equations by graphing 5th grade math math lowest common denominator length of a rectangle mathematical proofs quadratic functions diameter of a circle what is the answers? dividing polynomials derivative of a function vertex of a parabola calculus integers equation algebra 1 converting fractions to decimals evaluating functions algebra 2 perpendicular lines range of a function finding the nth term ordered pairs combining like terms least common denominator unit conversion radius of a circle calculators solve for y greatest to least ) complex numbers slope calculus problem because i don't understand solving radical equations area word problems 4th grade math functions please answer this question as soon as possible. thank you :) statistics math homework geometry word problems multiplying fractions calculate distance between two points common denominator absolute value ratios find out the answer equation of a tangent line binomial expansion help me please and show how to work it out round to the nearest tenth set builder notation percents simplifying radicals #math significant figures show work product of two consecutive numbers radicals adding fractions () midpoint of a line median graphing number patterns show every step to solve this problem divisibility rules solve place values pre-algebra problems graphing functions - (explain this to me) roots of polynomials factor by grouping 1 improper fractions to mixed numbers volume of a cylinder subtracting fractions maths percentage decimals derivatives expanded forms ? how to complete the square simultaneous equations numbers rational irrational numbers solving equations with variables = sets comparing decimals implicit differentiation compound interest need help solving quadratic equations by completing the square surface area of a prism multiplying polynomials integration http: mathhomeworkanswers.org ask?cat=# please help rounding decimals angles divide http: mathhomeworkanswers.org ask# perimeter of a triangle algebra1 pemdas trigonometry age problem solving trigonometric equations mixed numbers average rate of change chemistry logarithms rounding to the nearest cent 9th grade math matrices #help how do you solve this problem in distributive property geometry problem probability of an event surface area of a cube mean dividing measurement answer factor reducing frations to lowest terms arithmetic sequences direct variation height of a triangle lcm simplifying trigonometric equation using identities

Prove the quadratic equation

I need to understand the proof of the quadratic equation. I know that it can be done using a completing the square method.  Is it possible to do this quadratic equation proof without completing the square?
asked Apr 8, 2011 in Algebra 1 Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

A quadratic equation in the standard form is given by

ax 2 + bx + c = 0

where a, b and c are constants with a not equal to zero.
...Solve the above equation to find the quadratic fomulas

ax 2 + bx + c = 0

Divide all terms by a
x 2 + (b / a) x + c / a = 0

Subtract c / a from both sides
x 2 + (b / a) x + c / a - c / a = - c / a

and simplify
x 2 + (b / a) x = - c / a

Add (b / 2a) 2 to both sides
x 2 + (b / a) x + (b / 2a) 2 = - c / a + (b / 2a) 2

to complete the square
[ x + (b / 2a) ] 2 = - c / a + (b / 2a) 2

Group the two terms on the right side of the equation
[ x + (b / 2a) ] 2 = [ b 2 - 4a c ] / ( 4a2 )

Solve by taking the square root
x + (b / 2a) = ± sqrt { [ b 2 - 4a c ] / ( 4a2 ) }

Solve for x to obtain two solutions
x = - b / 2a ± sqrt { [ b 2 - 4a c ] / ( 4a2 ) }

The term sqrt { [ b 2 - 4a c ] / ( 4a2 ) } may be written
sqrt { [ b 2 - 4a c ] / ( 4a2 ) } = sqrt(b 2 - 4a c) / 2 | a |

Since 2 | a | = 2a when a > 0 and 2 | a | = -2a when a < 0, the two solutions to the quadratic equation may be written
x = [ -b + sqrt( b 2 - 4a c ) ] / 2 a

x = [ -b - sqrt( b 2 - 4a c ) ] / 2 a

The term b 2 - 4a c which is under the square root in both solutions is called the discriminant of the quadratic equation. It can be used to determine the number and nature of the solutions of the quadratic equation. 3 cases are possible

case 1: If b 2 - 4a c > 0 , the equation has 2 solutions.

case 2: If b 2 - 4a c = 0 , the equation has one solutions of mutliplicity 2.

case 3: If b 2 - 4a c < 0 , the equation has 2 imaginary solutions.

answered Apr 8, 2011 by mshelton Level 4 User (9,350 points)
Your c/a value is the product of the roots
Your -b/a value is the sum of your roots

Related questions

1 answer 25 views
1 answer 24 views
1 answer 40 views
2 answers 52 views
52 views asked Oct 27, 2013 in Other Math Topics by mathematical proof
0 answers 32 views
32 views asked Oct 21, 2013 in Other Math Topics by anonymous
0 answers 36 views
36 views asked Aug 15, 2013 in Other Math Topics by Shenbagavalli.N
0 answers 28 views