One of the solutions to x2 - 2x - 15 = 0 is x = -3. What is the other solution?
x = -5, x = -1, x = 1, x = 5
Solution:
Given that, x2 - 2x - 15 = 0
Let us solve this quadratic equation by splitting the middle term.
x2 - 5x -3x - 15 = 0
x(x - 5) - 3(x- 5) = 0
(x + 3)(x - 5) = 0
Therefore, the roots are (x + 3) = 0 ⇒ x = -3 and
(x - 5) = 0 ⇒ x = 5
Therefore, the other solution is x = 5.
Aliter
From the options given, substitute the values of x in the given quadratic equation, x2 - 2x - 15 = 0.
When x = -5,
L.H.S. = x2 - 2x - 15 = (-5)2 -2(-5) - 15 = 20
L.H.S. ≠ R.H.S.
When x = 5
L.H.S. = x2 - 2x - 15 = (5)2 -2(5) - 15 = 0
L.H.S. = R.H.S.
Therefore, the other solution is x = 5.
Aliter
Using the synthetic division method,
Remainder = 0
Quotient = x - 5
∴ x - 5 = 0 ⇒ x = 5
∴ The other solution is x = 5.
One of the solutions to x2 - 2x - 15 = 0 is x = -3. What is the other solution?
Summary:
If one of the solutions to x2 - 2x - 15 = 0 is x = -3, the other solution is x = 5.