Quadratic equation

Question

Write the quadratic equation whose roots are 2 and -6, and whose leading coefficient is 2. (Use the letter x to represent the variable. )

_ = 0

Answer 1

A quadratic equation can be expressed in the general form as follows: ax^2 + bx + c = 0. The roots of the quadratic equation are the solutions of this equation.

If we know the roots of the equation, we can express the quadratic equation as follows:

a(x - r1)(x - r2) = 0

where:

a is the leading coefficient,

r1 and r2 are the roots of the equation.

So if the roots of the equation are 2 and -6, and the leading coefficient is 2, we can plug these into the equation:

2(x - 2)(x - (-6)) = 0

which simplifies to:

2(x - 2)(x + 6) = 0

This then simplifies to:

2(x^2 + 4x - 12) = 0

and finally to:

2x^2 + 8x - 24 = 0

So, the quadratic equation with roots 2 and -6, and a leading coefficient of 2, is 2x^2 + 8x - 24 = 0.

Answer 2

y = a(x-r1)(x-r2) where r1 and r2 are the roots

y = 2(x-2)(x+6)