MHB Lacey's question at Yahoo Answers regarding a quadratic equation

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The quadratic equation -3x^2 - x - 5 = 0 can be transformed to 3x^2 + x + 5 = 0 by multiplying through by -1. The coefficients are identified as a = 3, b = 1, and c = 5, leading to a discriminant calculation of Δ = b² - 4ac = 1 - 60 = -59. Since the discriminant is negative, the equation has two complex conjugate roots. Using the quadratic formula, the roots are found to be x = (-1 ± i√59) / 6. This discussion highlights the importance of the discriminant in determining the nature of the roots of a quadratic equation.
MarkFL
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Here is the question:

Solve the quadratic equation?

Consider the following quadratic equation -3x^2-x-5=0

Use the discriminant b^2-4ac to determine the number of solutions of the quadratic equation

Solve using the quadratic equation usinf the formula y= (-b +/- √b^2-4ac) / 2a

Here is a link to the question:

Solve the quadratic equation? - Yahoo! Answers

I have posted a link there so the OP can find my response.
 
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Hello Lacey,

The first thing I would do is multiply through by -1, just to get rid of all those negative signs, as this will not change the value of the discriminant and roots:

$$3x^2+x+5=0$$

Now, we identify:

$$a=3,\,b=1,\,c=5$$

and the discriminant is:

$$\Delta=b^2-4ac=(1)^2-4(3)(5)=1-60=-59<0$$

Since the discriminant is negative, we know we will have two, complex conjugate roots.

Using the quadratic formula, we find that these roots are:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-1\pm\sqrt{-59}}{2(3)}=\frac{-1\pm i\sqrt{59}}{6}$$

To Lacey and any other guests viewing this topic, I invite and encourage you to post other such questions in our http://www.mathhelpboards.com/f2/ forum.

Best Regards,

Mark.
 
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