MATHEMATICS

JAMB 2022 - Question 9

Mathematics 2022 JAMB Past Questions - Question 9: If x = 1 is the root of the equation x³ -2x² - 5x +6, find the other roots

If x = 1 is the root of the equation x³ -2x² - 5x +6, find the other roots
A:
B:
C:
D:
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Correct Answer

C

Explanation

To find the other roots of the equation x³ - 2x² - 5x + 6, given that x = 1 is a root, we can use polynomial division or synthetic division to divide the polynomial by (x - 1). This will give us a quadratic equation, which we can then solve to find the remaining roots.Performing the division, we have:      x² - x - 6    ___________________x - 1 | x³ - 2x² - 5x + 6      - (x³ - x²)      _____________              - x² - 5x              + (x² - x)              _____________                      - 4x + 6                      + (4x - 4)                      _____________                            2The remainder is 2, which means that (x - 1) is not a factor of the polynomial.Now, we have the quadratic equation x² - x - 6 = 0. We can factorize it or use the quadratic formula to find the remaining roots.Factoring the quadratic equation, we have:(x - 3)(x + 2) = 0Setting each factor equal to zero, we get:x - 3 = 0 or x + 2 = 0Solving for x, we find:x = 3 or x = -2Therefore, the other roots of the equation x³ - 2x² - 5x + 6, given that x = 1 is a root, are x = 3 and x = -2.