5x² - 10x - 75 = 0
================
A quadratic equation with roots p and q can be written in the standard form ax² + bx + c = 0 as follows:
If we know the roots and the leading coefficient, a, we can find the other coefficients, b and c, using these properties:
- The coefficient b is -a times the sum of the roots;
- The coefficient c is a times the product of the roots.
From the question, it is revealed that:
- p = 5,
- q = -3, and the leading coefficient
- a = 5
Using the properties mentioned above,
To find b, we calculate:
- b = - a * (p + q) = -5 * (5 + -3) = -5 * 2 = -10
To find c, we calculate:
- c = a*p*q = 5 * 5 * (-3) = -75
Now that we have a, b, and c, we can write the quadratic equation: