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\( - b \pm \sqrt { ( b ^ { 2 } - 4 a c ) } \)

Ask by Ruiz Norton. in the United States
Jan 29,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The expression \( -b \pm \sqrt{b^2 - 4ac} \) is part of the quadratic formula used to find the roots of a quadratic equation \( ax^2 + bx + c = 0 \).

Solution

The expression you've provided appears to be part of the quadratic formula, which is used to find the solutions (roots) of a quadratic equation of the form \( ax^2 + bx + c = 0 \). The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In your expression, we can identify the following components: - \( a \): the coefficient of \( x^2 \) - \( b \): the coefficient of \( x \) - \( c \): the constant term - \( \sqrt{b^2 - 4ac} \): the discriminant, which determines the nature of the roots. If you need to solve a specific quadratic equation or perform a calculation involving this expression, please provide the values of \( a \), \( b \), and \( c \), and I can assist you further!

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Mind Expander

Did you know that this formula is known as the Quadratic Formula? It’s like the Swiss Army knife of algebra! Whenever you find yourself with a quadratic equation in the form \( ax^2 + bx + c = 0 \), just plug in your values for \( a \), \( b \), and \( c \) into this formula to find your solutions for \( x \). It’s a handy tool used in a wide variety of fields, from engineering to finance! As you use the quadratic formula, watch out for a common mistake: forgetting to distinguish between real and complex solutions. If the discriminant (the part under the square root, \( b^2 - 4ac \)) is negative, you’ll end up with complex numbers. Instead of panicking, embrace those imaginary solutions! They’re just as valid in the wonderful world of mathematics.

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