Explain how to find the values of a, b, and c, in a quadratic equation?
Answers
Step-by-step explanation:
4a+2b+6c=1
2a+6b+8c=-6
6a+8b+18c=-7
To find the values of a, b, and c in a quadratic equation, you can follow these steps:
A quadratic equation is an equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
Write down the quadratic equation in the form ax^2 + bx + c = 0.
Identify the values of a, b, and c by comparing the coefficients of x^2, x, and the constant term, respectively.
If the coefficient of x^2 is not equal to 1, divide both sides of the equation by this coefficient to obtain an equivalent equation with a leading coefficient of 1. For example, if the equation is 2x^2 + 4x - 6 = 0, divide both sides by 2 to get x^2 + 2x - 3 = 0.
Use the quadratic formula to solve for x, which is given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where sqrt denotes the square root function. Note that the quadratic formula can only be used for equations in the form ax^2 + bx + c = 0.
Once you have found the values of x, substitute them back into the original equation to find the values of a, b, and c. For example, if you found that x = 2 and x = -3, you can substitute these values into the equation x^2 + 2x - 3 = 0 to get:
a(2)^2 + b(2) + c = 0
a(-3)^2 + b(-3) + c = 0
Simplifying these equations and solving for a, b, and c will give you the values you are looking for.
Alternatively, if you know two roots of the quadratic equation, say x1 and x2, then you can use Vieta's formulas to find a, b, and c. Vieta's formulas state that:
a = 1
b = -(x1 + x2)
c = x1x2
These formulas are derived from the fact that the sum of the roots of a quadratic equation is -b/a and the product of the roots is c/a
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