If the equation 2x^2 + 3x + k = 0 has roots 1 and -2, what is the value of k?

If the equation 2x^2 + 3x + k = 0 has roots 1 and -2, what is the value of k?

Correct Answer: -4

Step 1: Understand that the equation 2x^2 + 3x + k = 0 is a quadratic equation.
Step 2: Recognize that the roots of the equation are given as 1 and -2.
Step 3: Use Vieta's formulas, which tell us that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is equal to -b/a and the product of the roots (r1 * r2) is equal to c/a.
Step 4: Calculate the sum of the roots: 1 + (-2) = -1.
Step 5: Calculate the product of the roots: 1 * (-2) = -2.
Step 6: According to Vieta's formulas, the product of the roots (r1 * r2) = k/a. Here, a = 2, so we have -2 = k/2.
Step 7: Solve for k by multiplying both sides of the equation by 2: k = -2 * 2.
Step 8: Calculate k: k = -4.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
Quadratic Equations – Understanding the standard form of a quadratic equation and how to find its roots.