Question

Write a quadratic equation that has the given solutions:

The solutions:
1) x = 7, x = −3
2) x = −9, x = 10
3) x = 1, x = 4

Answer 1

To write a quadratic equation with given solutions, use the factored form of a quadratic equation. The factored form of the equation for the first set of solutions x = 7, x = -3 is (x - 7)(x + 3) = 0, which expands to x^2 - 4x - 21 = 0. Similar steps can be followed for other sets of solutions.

Step-by-step explanation:

To write a quadratic equation with the given solutions, we need to use the factored form of a quadratic equation. The factored form is (x - r)(x - s) = 0, where r and s are the solutions.

Let's take the first set of solutions as an example: x = 7, x = -3. The factored form of the equation would be (x - 7)(x + 3) = 0. Expanding this equation gives us x^2 - 4x - 21 = 0.

Similarly, for the second set of solutions x = -9, x = 10, the factored form is (x + 9)(x - 10) = 0, which expands to x^2 - x - 90 = 0.

Lastly, for the third set of solutions x = 1, x = 4, the factored form is (x - 1)(x - 4) = 0, which expands to x^2 - 5x + 4 = 0.