Formula Cuadratica
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Publicado: 27 de enero de 2013
The Quadratic Formula
Quadratic equations have just one unknown, but contain a square term as well as linear terms.
For example, [pic] is a quadratic equation in x
[pic] is a quadraticequation in t.
There is a formula for finding the unknown value, but before it can be used the equation must be written with all of its terms at one side of the equation i.e. in the form [pic] where a,b and c are known positive or negative numbers and x is the unknown value.
This formula gives two possible values for x. Usually in practical situations it will be obvious whichanswer is the correct one, but in some contexts both answers give possible solutions.
Example 1 Solve the equation [pic]
How to do it…
Rearrange the equation so all terms are at one side:In this case subtract 3: [pic]
Write down the values of a, b and c: a = 2, b = 1 and c = – 3
Substitute these values into the formula: [pic]
Work out the values in the square root anddenominator first: [pic]
Take the square root (note it is not always a round number): [pic]
Split the formula into two, using + in one and – in the other: [pic] or [pic]
Work out theanswers: [pic] or [pic]
The solutions are x = 1 and – 1.5
Check each answer in the original equation:
Substituting x = 1 into [pic] gives [pic] Correct!
Substituting x =– 1.5 into [pic] gives [pic] Correct!
Example 2 Solve the equation [pic]
How to do it…
The working is usually easier if the squared term is positive.
Write the equation the other wayround: [pic]
Subtract 7t: [pic]
Take care when writing down the values of a, b and c: a = 5, b = – 7 and c = 1
Substitute these values into the formula: [pic]
Work out thevalues in the square root and denominator: [pic]
When the square root is not exact, round it to about 4 figures: [pic]
Split the formula into two: [pic] or [pic]
Work out the...
Quadratic equations have just one unknown, but contain a square term as well as linear terms.
For example, [pic] is a quadratic equation in x
[pic] is a quadraticequation in t.
There is a formula for finding the unknown value, but before it can be used the equation must be written with all of its terms at one side of the equation i.e. in the form [pic] where a,b and c are known positive or negative numbers and x is the unknown value.
This formula gives two possible values for x. Usually in practical situations it will be obvious whichanswer is the correct one, but in some contexts both answers give possible solutions.
Example 1 Solve the equation [pic]
How to do it…
Rearrange the equation so all terms are at one side:In this case subtract 3: [pic]
Write down the values of a, b and c: a = 2, b = 1 and c = – 3
Substitute these values into the formula: [pic]
Work out the values in the square root anddenominator first: [pic]
Take the square root (note it is not always a round number): [pic]
Split the formula into two, using + in one and – in the other: [pic] or [pic]
Work out theanswers: [pic] or [pic]
The solutions are x = 1 and – 1.5
Check each answer in the original equation:
Substituting x = 1 into [pic] gives [pic] Correct!
Substituting x =– 1.5 into [pic] gives [pic] Correct!
Example 2 Solve the equation [pic]
How to do it…
The working is usually easier if the squared term is positive.
Write the equation the other wayround: [pic]
Subtract 7t: [pic]
Take care when writing down the values of a, b and c: a = 5, b = – 7 and c = 1
Substitute these values into the formula: [pic]
Work out thevalues in the square root and denominator: [pic]
When the square root is not exact, round it to about 4 figures: [pic]
Split the formula into two: [pic] or [pic]
Work out the...
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