Given the quadratic equation ax2 + 10x + 2 = 0, determine all values of a that will result in this equation having non-real solutions. Show all work that leads to your answer.

a>12.5.

Step-by-step explanation:

you need to look at the discriminant in the quadratic formula:

coming from the quadratic polynomial

In our case, b=10 and c=2, hence, the discriminant is

We will obtain non-real values if the discriminant is less than zero.

Therefore, this condition is written as

and we must solve for a. It yields

Hence, the answer is a>12.5.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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step-by-step explanation:

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