Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.

Front

What do the symbols a, b, and c represent in a quadratic equation?

Back

In the quadratic equation ax^2 + bx + c = 0, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.

Front

How do you identify the coefficients in the equation 2x^2 - 3x - 5 = 0?

Back

For the equation 2x^2 - 3x - 5 = 0, a = 2, b = -3, and c = -5.

Front

What is the discriminant in the quadratic formula and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root, b^2 - 4ac. It indicates the nature of the roots: if positive, there are two real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you solve the quadratic equation 5x^2 + 3x - 3 = 0 using the quadratic formula?

Back

To solve 5x^2 + 3x - 3 = 0, identify a = 5, b = 3, c = -3, then apply the quadratic formula: x = \frac{-3 \pm \sqrt{3^2 - 4(5)(-3)}}{2(5)} = \frac{-3 \pm \sqrt{69}}{10}.

Front

What are the roots of the equation x^2 - 6x + 4 = 0?

Back

The roots of the equation x^2 - 6x + 4 = 0 can be found using the quadratic formula: x = 3 \pm \sqrt{5}.

Front

What is the significance of the '±' symbol in the quadratic formula?

Back

The '±' symbol indicates that there are two possible solutions for x, one for the addition and one for the subtraction.

Front

How can you determine if a quadratic equation has real or complex roots?

Back

You can determine the nature of the roots by calculating the discriminant (b^2 - 4ac). If the discriminant is positive, the roots are real; if it is zero, there is one real root; if negative, the roots are complex.

Front

What is the first step in solving a quadratic equation using the quadratic formula?

Back

The first step is to rearrange the equation into the standard form ax^2 + bx + c = 0, identifying the coefficients a, b, and c.

Front

How do you simplify the expression \sqrt{b^2 - 4ac} when solving a quadratic equation?

Back

To simplify \sqrt{b^2 - 4ac}, calculate the value of b^2 - 4ac first, then take the square root of that result.