THE Bhaskara's formula is one of the best known methods to find the roots of a equationofseconddegree. In this formula, just replace the values of the coefficients of this equation and perform the calculations that are formed.
Remember: solving an equation is finding the values of x that make that equation true. To the equationsofseconddegree, are synonymous with solving: meet at roots or find the zeros of the equation.
To make it easier to understand the use of formulainBhaskara, it is worth remembering what a equationofseconddegree and what are its coefficients.
Second degree equation
An equation of seconddegree is all that can be written in the following way:
ax2 + bx + c = 0
With a, b and c as real numbers and with a ≠ 0.
If x is the unknown of the equationofsecond degree above then The, B and ç are your coefficients. The unknown is the unknown number in an equation, and the coefficients are the known numbers in most cases.
Note that the coefficient “a” is the real number that multiplies x2. For the use of formulainBhaskara, this will always be true.
Also, the coefficient "b" is the real number that multiplies x, and the coefficient "c" is the fixed portion that appears in the equation, that is, that does not multiply the unknown.
Knowing this, we can say that the coefficients gives equation:
4x2 – 4x – 24 = 0
They are:
a = 4, b = – 4 and c = – 24
Mind Map: Formula of Bhaskara
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discriminating
The first step to be taken to solve a equationofseconddegree is to calculate the value of your discriminating. To do this, use the formula:
? = b2 – 4·a·c
In that formula,? it's the discriminating and The, B and ç are the coefficients of equationofseconddegree.
The discriminant of the example given above, 4x2 – 4x – 24 = 0, it will be:
? = b2 – 4·a·c
? = (– 4)2 – 4·4·(– 24)
? = 16– 16·(– 24)
? = 16 + 384
? = 400
Therefore, we can say that the discriminating of the 4x equation2 – 4x – 24 = 0 is ? = 400.
Bhaskara's formula
having in hand the coefficients it's the discriminating of a equationofseconddegree, use the formula below to find your results.
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x = – b ± √?
2nd
Note that there is an ± sign before the root. This means that there will be two results for this equation: one for – √? and another for + √?.
Still using the previous example, we know that, in the equation 4x2 – 4x – 24 = 0, the coefficients they are:
a = 4, b = – 4 and c = – 24
And the value of delta é:
? = 400
Replacing these values in the formulainBhaskara, we will have the two results sought:
x = – b ± √?
2nd
x = – (– 4) ± √400
2·4
x = 4 ± 20
8
The first value will be called x’, and we will use the positive result of √400:
x’ = 4 + 20
8
x’ = 24
8
x’ = 3
The second value will be called x’’, and we will use the negative result of √400:
x’ = 4– 20
8
x’ = – 16
8
x’ = – 2
So the results - also called roots or zeros - of that equation they are:
S = {3, - 2}
2nd Example: What are the measurements of the sides of a rectangle whose base is twice the width and its area is equal to 50 cm2.
Solution: If the base measures twice the height, it can be said that if the height measures x the base will measure 2x. As the area of a rectangle is the product of its base and height, we will have:
A = 2x·x
Replacing the values and solving the multiplication, we will have:
50 = 2x2
or
2x2 – 50 = 0
Note that this equationofseconddegree have the coefficients: a = 2, b = 0 and c = – 50. Replacing these values in the formula of discriminating:
? = b2 – 4·a·c
? = (0)2 – 4·2·(– 50)
? = 0– 8·(– 50)
? = 400
Replacing the coefficients and the discriminant in formulainBhaskara, we will have:
x = – b ± √?
2nd
x = – (0) ± √400
2·2
x = 0 ± 20
4
For x’, we will have:
x’ = 20
4
x’ = 5
For x’’, we will have:
x’ = – 20
4
x’ = – 5
S = {5, – 5}
This is the solution of equationofseconddegree. Since there is no negative length for one side of a polygon, the solution to the problem is x = 5 cm for the short side, and 2x = 10 cm for the long side.
By Luiz Paulo Moreira
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
SILVA, Luiz Paulo Moreira. "What is the formula of Bhaskara?"; Brazil School. Available in: https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-formula-bhaskara.htm. Accessed on June 27, 2021.
