Question

Explain how to find the solution to a quadratic equation with imaginary numbers using a calculator.

Answer 1

To solve a quadratic equation with imaginary numbers using a calculator, follow these steps: write down the equation, enter the coefficients into the calculator, use the quadratic formula to calculate the solutions, and round the solutions if necessary.

Step-by-step explanation:

To solve a quadratic equation with imaginary numbers using a calculator, follow these steps:

1. Write down the equation in the form ax^2 + bx + c = 0, where a, b, and c are coefficients.
2. Enter the values of a, b, and c into your calculator.
3. Use the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), to calculate the solutions.
4. If the discriminant, b^2 - 4ac, is negative, you will get imaginary solutions.
5. Round the solutions to the desired decimal places, if necessary.

For example, let's solve the equation 2x^2 + 5x + 3 = 0:

1. Enter the values a = 2, b = 5, and c = 3 into your calculator.
2. Use the quadratic formula to get x = (-5 ± √(5^2 - 4(2)(3)))/(2(2)).
3. Simplifying, you get x = (-5 ± √(25 - 24))/(4), which becomes x = (-5 ± √(1))/(4).
4. Since the discriminant is positive, the solutions are real.
5. Rounding to two decimal places, you get x = (-5 + 1)/(4) = -1 and x = (-5 - 1)/(4) = -1.5.