What is the slope of a line parallel to the line with equation y = 5x – 2 A:5
B:-1/-5
C:-2
D:-5

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Ответ:

titocerber

14.11.2021

Mathematics

$\left \{ {{x_{1} =+\sqrt{7} } \atop {x_{2} =-\sqrt{7}}} \right.$

$\left \{ {{x_{3} =+\sqrt{2}i } \atop {x_{4} =-\sqrt{2}i}} \right.$

Step-by-step explanation:

The given equation is

$x^{4}-5x^{2} -14=0$

To factor this expression, we can change variables to make easier to see the solution.

$x^{4}=y^{2}$ and $x^{2} = y$

Applying the change, we have

$y^{2}-5y-14=0$

Now, you can observe that to factor this expression, we just need to find two number which product is 14 and which difference is 5, such numbers are 7 and 2.

$y^{2}-5y-14=(y-7)(y+2)$

However, remember that $y=x^{2}$ , so

$x^{4}-5x^{2} -14=(x^{2}-7 )(x^{2}+2)=0$

Applying the zero property, we have

$x^{2} -7=0 \implies x^{2} =7 \implies \left \{ {{x_{1} =+\sqrt{7} } \atop {x_{2} =-\sqrt{7}}} \right.$

$x^{2} +2=0 \implies x^{2} =-2 \implies \left \{ {{x_{3} =+\sqrt{2}i } \atop {x_{4} =-\sqrt{2}i}} \right.$

As you can see, the equation has two real solutions and two complex solutions.

Therefore, the right answer is the last choice.

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What is the slope of a line parallel to the line with equation y = 5x – 2 A:5 B:-1/-5 C:-2 D:-5