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Please help me with this problem:Consider the quadratic equation 3x^2 - 6 = 2x.(a)What is the value of the discriminant?(b)What does the discriminant of the quadratic equation tell about the solutions to 3x^2 - 6 = 2x ?

Please help me with this problem:Consider the quadratic equation 3x^2 - 6 = 2x.(a-example-1
User Mlegg
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1 Answer

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Consider the general quadratic equation:


ax^2+bx+c=0

The discriminant of this equation is defined as:


d=b^2-4ac

(a) Calculate the discriminant. Before we can use the formula, we need to transform the equation into the required form.

We are given:


3x^2-6=2x

Subtracting 2x and rearranging:


3x^2-2x-6=0

We can now identify the coefficients: a = 3, b = -2, c = -6, and compute the discriminant as follows:


\begin{gathered} d=(-2)^2-4*3*(-6) \\ d=4+72 \\ \boxed{d=76} \end{gathered}

(b) The discriminant gives important information about the solutions of the equation:

* If d is zero, there is only one real solution.

* If d is positive, there are two real solutions.

* If d is negative, there are two complex solutions.

In our equation, d is positive and the equation has two real solutions

User Rovak
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