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Question 8
$1 \mathrm{pts}$
Which of the given quadratic equations has root $x=-i \sqrt{5}$ ? Select all that apply.
$y=x^{2}+5$
$y=x^{2}-5$
$y=-x^{2}-5$
$y=x^{2}-25$
$y=-5 x^{2}-25$
$y=(x+5)^{2}$
$y=-x^{2}-25$

Answer

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Answer

$\boxed{y=x^{2}+5, y=-x^{2}-5, y=-5 x^{2}-25}$

Steps

Step 1 ：Plug the value $x = -i\sqrt{5}$ into each equation and see if it satisfies the equation.

Step 2 ：$y=(-i\sqrt{5})^2+5$ is satisfied

Step 3 ：$y=-(-i\sqrt{5})^2-5$ is satisfied

Step 4 ：$y=-5(-i\sqrt{5})^2-25$ is satisfied

Step 5 ：$\boxed{y=x^{2}+5, y=-x^{2}-5, y=-5 x^{2}-25}$