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sladkih [1.3K]
4 years ago
15

The product of two consecutive, negative integers is 182. What equation represents the situation?

Mathematics
2 answers:
OLEGan [10]4 years ago
5 0

Answer:

-14,-13

Step-by-step explanation:

Sholpan [36]4 years ago
4 0
-13 and -14

They both are consecutive negative integers that multiply to 182.
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{ \qquad\qquad\huge\underline{{\sf Answer}}}

Let's solve ~

Calculate discriminant :

\qquad \sf  \dashrightarrow \: 3 {x}^{2}  + 6x - 1

  • a = 3
  • b = 6
  • c = 1

\qquad \sf  \dashrightarrow \: discriminant =  {b}^{2}  - 4ac

\qquad \sf  \dashrightarrow \: d = (6) {}^{2}  - (4 \times 3 \times 1)

\qquad \sf  \dashrightarrow \: d = 36 - 12

\qquad \sf  \dashrightarrow \: d = 24

\qquad \sf  \dashrightarrow \:  \sqrt {d} = 2 \sqrt{6}

Now, let's calculate it's roots ( x - intercepts )

\qquad \sf  \dashrightarrow \: x =  \cfrac{ - b  \pm \sqrt{d} }{2a}

\qquad \sf  \dashrightarrow \: x =  \cfrac{ - 6\pm 2 \sqrt{6}  }{2 \times 3}

\qquad \sf  \dashrightarrow \: x =  \cfrac{ - 6\pm 2 \sqrt{6}  }{6}

So, the intercepts are :

\qquad \sf  \dashrightarrow \: x =  \cfrac{ - 6 -  2 \sqrt{6}  }{6}

and

\qquad \sf  \dashrightarrow \: x =  \cfrac{ - 6  +  2 \sqrt{6}  }{6}

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Step-by-step explanation:

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