Question

find the discriminant,
6w² + 3 = 2w
what type of solutions does the equation have?
one real solution two real solutions
two complex (non-real)
solutions

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\). Given the equation \(6w^{2}+3 = 2w\), we can rewrite it as \(6w^{2}-2w + 3=0\). Here, \(a = 6\), \(b=- 2\), and \(c = 3\).

Step2: Calculate the discriminant

The formula for the discriminant (\(D\)) of a quadratic equation \(ax^{2}+bx + c = 0\) is \(D=b^{2}-4ac\). Substitute \(a = 6\), \(b=-2\), and \(c = 3\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Determine the type of solutions

• If \(D>0\), the equation has two real solutions.
• If \(D = 0\), the equation has one real solution.
• If \(D<0\), the equation has two complex (non - real) solutions.

Since \(D=-68<0\), the equation has two complex (non - real) solutions.

Answer:

The discriminant is \(-68\) and the equation has two complex (non - real) solutions.