What is the discriminant of -9x^2+10x=-2x+4−9x2+10x=−2x+4 and what does that mean?

1 Answer
Alan P. · Chaoyi Z.
Jul 22, 2015

00
It means that there is exactly 1 Real solution for this equation

Explanation:

The discriminant of a quadratic equation is b^2 – 4ac. To calculate the discriminant of the equation you provided, we move -2x and 4 to the left, resulting in -9x^2+12x-4. To calculate the discriminant of this simplified equation, we use our formula above, but substitute 12 for b, -9 as a, and -4 as c.

We get this equation: (12)^2 - 4(-9)(-4), which evaluates to 0

The "meaning" is the result of the discriminant being a component of the quadratic formula for the solution(s) to quadratic equation in the form:
color(white)("XXXX")ax^2+bx+c=0
where the solutions can be determined by:
color(white)("XXXX")x=(-b+-sqrt(b^2-4ac))/(2a)

Notice that the discriminant is the component within the square root, and as a result:
"discriminant" { (= 0, " one Real root"), (< 0, " no Real Roots"), (> 0, " two Real roots") :}

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