Connect with knowledgeable individuals and get your questions answered on IDNLearn.com. Ask any question and get a detailed, reliable answer from our community of experts.
Sagot :
To solve the quadratic equation [tex]\( x^2 + 121 = 0 \)[/tex], let's follow a step-by-step approach:
1. Rewrite the equation:
[tex]\[ x^2 + 121 = 0 \][/tex]
2. Isolate [tex]\( x^2 \)[/tex] by subtracting [tex]\( 121 \)[/tex] from both sides:
[tex]\[ x^2 = -121 \][/tex]
3. Take the square root of both sides:
[tex]\[ x = \pm\sqrt{-121} \][/tex]
4. Simplify the expression under the square root:
Notice that [tex]\( -121 \)[/tex] can be written as [tex]\( -1 \times 121 \)[/tex]. Therefore,
[tex]\[ \sqrt{-121} = \sqrt{-1 \times 121} = \sqrt{-1} \times \sqrt{121} \][/tex]
5. Use the fact that [tex]\( \sqrt{-1} \)[/tex] is defined as [tex]\( i \)[/tex] (the imaginary unit):
[tex]\[ \sqrt{-121} = i \times 11 = 11i \][/tex]
6. So, the solutions will be:
[tex]\[ x = \pm 11i \][/tex]
Thus, the solutions to the equation [tex]\( x^2 + 121 = 0 \)[/tex] are [tex]\( 11i \)[/tex] and [tex]\( -11i \)[/tex], which corresponds to option:
D. [tex]\( -11i, 11i \)[/tex]
1. Rewrite the equation:
[tex]\[ x^2 + 121 = 0 \][/tex]
2. Isolate [tex]\( x^2 \)[/tex] by subtracting [tex]\( 121 \)[/tex] from both sides:
[tex]\[ x^2 = -121 \][/tex]
3. Take the square root of both sides:
[tex]\[ x = \pm\sqrt{-121} \][/tex]
4. Simplify the expression under the square root:
Notice that [tex]\( -121 \)[/tex] can be written as [tex]\( -1 \times 121 \)[/tex]. Therefore,
[tex]\[ \sqrt{-121} = \sqrt{-1 \times 121} = \sqrt{-1} \times \sqrt{121} \][/tex]
5. Use the fact that [tex]\( \sqrt{-1} \)[/tex] is defined as [tex]\( i \)[/tex] (the imaginary unit):
[tex]\[ \sqrt{-121} = i \times 11 = 11i \][/tex]
6. So, the solutions will be:
[tex]\[ x = \pm 11i \][/tex]
Thus, the solutions to the equation [tex]\( x^2 + 121 = 0 \)[/tex] are [tex]\( 11i \)[/tex] and [tex]\( -11i \)[/tex], which corresponds to option:
D. [tex]\( -11i, 11i \)[/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.