Write the quadratic equation in standard form that has the given solutions.
x:{5, -3}
if x = 5 or x = -3
then the equation could be
(x-5)(a+3) = 0
or
x^2 - 2x - 15 = 0
If the solutions to a quadratic equation are x = 3 and x = -5, write the quadratic equation
To find the quadratic equation with the given solutions, you can use the fact that the solutions of a quadratic equation can be represented by the roots of the equation. The standard form of a quadratic equation is:
ax^2 + bx + c = 0
Given that the two solutions are x = 5 and x = -3, we can write two separate equations using these values:
(x - 5) = 0
(x + 3) = 0
To find the quadratic equation, we can multiply these two equations together:
(x - 5)(x + 3) = 0
Expanding this equation gives us:
x^2 + 3x - 5x - 15 = 0
Combining like terms, we get:
x^2 - 2x - 15 = 0
Therefore, the quadratic equation in standard form with the given solutions is:
x^2 - 2x - 15 = 0
To write a quadratic equation in standard form, we need to know the solutions or roots of the equation. The solutions of a quadratic equation can be represented as x-intercepts on the graph of the equation, where the curve intersects the x-axis.
Given that the solutions are x = 5 and x = -3, we can set up two linear factors representing these solutions:
(x - 5) and (x + 3)
Multiplying these factors together will give us the quadratic equation.
(x - 5)(x + 3)
To expand this expression, we can use the FOIL method:
x * x = x^2
x * 3 = 3x
-5 * x = -5x
-5 * 3 = -15
Combining these terms, we get:
x^2 + 3x - 5x - 15
Simplifying further gives us:
x^2 - 2x - 15
Therefore, the quadratic equation in standard form with the given solutions x = 5 and x = -3 is:
x^2 - 2x - 15 = 0