Complex Numbers, solving quadratic equations & comp the SQ

Front

What are the solutions to the equation (x + 2)(x - 3) = 0?

Back

The solutions are x = -2 and x = 3.

Front

How do you solve the quadratic equation 4x^2 - 9 = 0?

Back

The solutions are x = 3/2 and x = -3/2.

Front

What is the formula to calculate the new C-term in completing the square?

Back

C = (b/2)^2.

Front

What is the value of i in complex numbers?

Back

i = √(-1).

Front

What is the value of i^2?

Back

i^2 = -1.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b^2 - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

Front

How can you express a complex number in standard form?

Back

A complex number is expressed in standard form as a + bi, where a is the real part and b is the imaginary part.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.