Quadratic Equation

Question

Write the quadratic equation whose roots are −1 and 5 , and whose leading coefficient is 3. Use the letter X to represent the variable.

Please explain?

Answer 1

Hello, Adward,

A quadratic equation having the form Ax^2 +Bx +c = 0 that contains roots -1 and 5 should contain the factors (x +1) and (x-5). Let's multiply those two together:

= x^2 - 4x -5

That contains the roots -1 and 5.

But we need the leading coefficient to be 3, so multiply by 3:

= 3x^2 - 12x -15

That meets all the requirements.

Bob