Question

3. Find the value of m for which the equation mx + 14 = 12 + 2 has one repeated root.

Answer 1

Using the discriminant of a quadratic equation, it is found that the quadratic equation would have one repeated solution for m = -3.

What is the quadratic equation?

The quadratic equation is given as follows:

mx² + 12x - 12.

What is the discriminant of a quadratic equation and how does it influence the solutions?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

• If $\mathbf{\Delta > 0}$, it has 2 real solutions.

• If $\mathbf{\Delta = 0}$, it has 1 real solutions.

• If $\mathbf{\Delta < 0}$, it has 2 complex solutions.

For this problem, the coefficients are:

a = m, b = 12, c = -12.

Hence the discriminant is:

b² - 4ac = 144 + 48m.

We want it to be of 0, hence:

144 + 48m = 0

m = -144/48

m = -3.

More can be learned about the discriminant of a quadratic equation at brainly.com/question/19776811

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