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How do you find the value of the discriminant $- 4 r^{2} - 4 r = 6$ ?

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−80

−70

−20

answer is B.

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Detailed Solution

To find the value of the discriminant we have to make the given expression in the form of

a x^{2} + bx + c

. So, by taking all the terms on one side, and rearranging the equation in order, we will get the equation as

\Rightarrow - 4 r^{2} - 4 r - 6 = 0

And we know the formula to find the value of the discriminant

(△) = b^{2} - 4 ac △

.
Now, by comparing the given expression with

a x^{2} + bx + c

, we get the value of a,b, and c. Therefore,

a = 4, b = 4, and c = 6

.
Now, by substituting the values of a, b, and c in the expression of discriminant that is

(△) = b^{2} - 4 ac △

we get

\Rightarrow △ = 4^{2} - 4 \times 4 \times 6

\Rightarrow △ = 16 - 96

\Rightarrow △ = - 80

Thus, in solving

- 4 r^{2} - 4 r = 6

the value of the discriminant we get −80.

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