Question

Write the quadratic equation whose roots are 5 and -3, and whose leading coefficient is 5.​

Answer 1

5x² - 10x - 75 = 0

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A quadratic equation with roots p and q can be written in the standard form ax² + bx + c = 0 as follows:

• a(x - p)(x - q) = 0

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:

• 5x² - 10x - 75 = 0