Ask Question
6 September, 20:02

Wilma and Greg were trying to solve the quadratic equation x^2 + bx + c = 0. Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 1 and 6. Greg wrote down the wrong value of c (but his value of b was correct), and found the roots to be - 1 and - 4. What are the actual roots of x^2 + bx + c = 0?

+5
Answers (1)
  1. 7 September, 00:00
    0
    The roots are - 2 and - 3

    Step-by-step explanation:

    For a quadratic equation given as x² + bx + c, for roots x and y, the sum of roots is equal to the negation of the coefficient of the second term (i. e x + y = - b) while the products of the roots is equal to the coefficient of the second term (i. e x * y = c).

    Since for the roots 1 and 6, only the value of c was correct, to get c we use the product of roots. Therefore, c = 1 * 6 = 6

    Since for the roots - 1 and - 6, only the value of b was correct, to get b we use the sum of roots. Therefore:

    -b = - 1 + - 4 = - 5

    b = 5

    Since the quadratic equation is x² + bx + c, substituting value of b and c and solving:

    x² + 5x + 6 = 0

    x² + 2x + 3x + 6 = 0

    x (x + 2) + 3 (x + 2) = 0

    (x + 2) (x + 3) = 0

    x = - 2 or x = - 3

    The roots are - 2 and - 3
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Wilma and Greg were trying to solve the quadratic equation x^2 + bx + c = 0. Wilma wrote down the wrong value of b (but her value of c was ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers