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Marianna [84]
3 years ago
5

Use the discriminant to determine the number of real solutions to the equation. −4x^2=−8−10x

Mathematics
2 answers:
ICE Princess25 [194]3 years ago
6 0

Answer:

4

Step-by-step explanation:

Len [333]3 years ago
6 0

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

b^2-4ac. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

-4x^2=-8-10x but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

-4x^2+10x+8=0

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

10^2-4(-4)(8) which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

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