Use the discriminant to determine the number of real solutions to the equation. −4x^2=−8−10x
2 answers:
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:
. 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:
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:
From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:
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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Answer:
<h2>140 minutes</h2>Step-by-step explanation:
this problem focuses on the combined work rate
both can finish the work under 63 minute
let bobby mow the lawn in x minute
Billy will then mow the lawn in x-25 minutes
Let the completed job = 1 (a mowed lawn)
we can now apply the combined work formula for the two boys as
multiplying through by x(x-25 )we have
open bracket we have
rearranging and collecting like terms we have
we can now use the quadractic formula
a= 1
b= -151
c= 1575
the first answer x= 139.72 approximately 140 minutes mins is correct for Bobby's time
let us check
we can see that the solution approximates to 1