If the equation 2x^2 + 3x + k = 0 has roots 1 and -2, what is the value of k?
Practice Questions
1 question
Q1
If the equation 2x^2 + 3x + k = 0 has roots 1 and -2, what is the value of k?
-4
0
2
4
Using Vieta's formulas, k = 2*1*(-2) = -4.
Questions & Step-by-step Solutions
1 item
Q
Q: If the equation 2x^2 + 3x + k = 0 has roots 1 and -2, what is the value of k?
Solution: Using Vieta's formulas, k = 2*1*(-2) = -4.
Steps: 8
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.
