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Front

What is the quadratic formula used to find the solutions of a quadratic equation?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.

Front

How do you multiply two complex numbers in the form (a + bi)(c + di)?

Back

To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi². Remember that i² = -1.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

How do you express a percentage increase in a population over time?

Back

To express a percentage increase in a population, use the formula P(t) = P0(1 + r)^t, where P0 is the initial population, r is the growth rate (as a decimal), and t is the time in years.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are two complex roots.

Front

How do you convert an annual interest rate to a monthly rate for compounding?

Back

To convert an annual interest rate to a monthly rate, divide the annual rate by 12. For example, an annual rate of 7.5% becomes 7.5% / 12 = 0.625% per month.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is N(t) = N0e^(kt), where N0 is the initial quantity, k is the growth constant, and t is time.

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots of a quadratic equation by factoring, express the equation in the form ax² + bx + c = 0, factor it into (px + q)(rx + s) = 0, and then set each factor to zero to solve for x.

Front

What is the relationship between the roots and coefficients of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

How do you calculate the future value of an investment with compound interest?

Back

To calculate the future value of an investment with compound interest, use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.