Final answer:
To convert a quadratic equation to the standard form of ax^2 + bx + c = 0, subtract constants, divide by the coefficient of the quadratic term if necessary, or complete the square. The quadratic formula can then be used to find the roots of the equation.
Step-by-step explanation:
The question is asking for the correct method to convert a quadratic equation to standard form. There are several steps involved, depending on the initial format of the equation, but the standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. We need to ensure that the equation looks like this by organizing and simplifying the terms as necessary.
- A) To convert a quadratic equation to standard form, you might need to subtract the constant term from both sides if it's not already on one side of the equation.
- B) If the coefficient of the quadratic term (a) is not 1, you may need to divide each term by this coefficient to standardize the equation.
- C) Not all quadratic equations start in standard form; some may need to be rearranged or manipulated to reach standard form.
- D) Completing the square is another method that can be used to rewrite the equation in standard form, especially when it is useful to express the quadratic term as a square of a binomial.
To solve the given equation, x^2 + 1.2 x 10^-2x - 6.0 × 10^-3 = 0, we could use the quadratic formula, which efficiently finds the roots of any quadratic equation in standard form. Remember that the quadratic formula is given by the expression: -b ± √(b^2 - 4ac) / (2a).
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