How do I write a quadratic equation having the given numbers as solutions of
-9 and 3
(x+9)(x-3) = 0
expand it.
To write a quadratic equation with the given solutions of -9 and 3, you can use the factored form of a quadratic equation:
(x - r1)(x - r2) = 0
where r1 and r2 are the solutions. In this case, r1 = -9 and r2 = 3.
Substituting these values, the factored form becomes:
(x - (-9))(x - 3) = 0
(x + 9)(x - 3) = 0
Now, expand the equation:
x * x - x * 3 + 9 * x - 9 * 3 = 0
x^2 - 3x + 9x - 27 = 0
x^2 + 6x - 27 = 0
Hence, the quadratic equation with -9 and 3 as solutions is:
x^2 + 6x - 27 = 0
To write a quadratic equation with -9 and 3 as solutions, you can use the fact that the solutions of a quadratic equation are the values for which the equation equals zero.
To start, we know that if -9 is a solution, then (x + 9) must be a factor of the quadratic equation. Similarly, if 3 is a solution, then (x - 3) must also be a factor.
To obtain the quadratic equation, we can multiply these two factors:
(x + 9)(x - 3) = 0
Now, we can expand the equation to get the quadratic form:
x^2 - 3x + 9x - 27 = 0
Combining like terms, we have:
x^2 + 6x - 27 = 0
Therefore, the quadratic equation with -9 and 3 as solutions is:
x^2 + 6x - 27 = 0.