If one of the solutions to the equation x² + 2x – 15 = 0 is x = 3, what is the other solution?

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To find the other solution of the quadratic equation x² + 2x – 15 = 0, we can use the fact that quadratic equations can often be factored or solved using the quadratic formula.

Since we already know one solution is x = 3, we can use this information to find the other solution. First, let’s factor the equation based on its roots. If one root is x = 3, we can express the quadratic in a factored form:

We know that if x = 3 is a solution, 3 should satisfy the following equation:

x² + 2x - 15 = (x - 3)(x + b) = 0

Here, b is the other root we are trying to find. To determine b, we can use the fact that the product of the roots of the quadratic equation ax² + bx + c = 0 is given by:

product of the roots = c/a

In our equation:

  • a = 1
  • c = -15

Thus, the product of the roots (3 and the other root, which we’ll call r) is:

3 × r = -15

To solve for r, we can rearrange this equation:

r = -15 / 3 = -5

Therefore, the other solution to the equation x² + 2x – 15 = 0 is x = -5.

In conclusion, the two solutions to the quadratic equation are:

  • x = 3
  • x = -5

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