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Lisa [10]
3 years ago
9

A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Selec

t one answer for question A, and select one answer for question B. B: (x+3)(x−3) B: (x+3i)(x−3i) B: (x−3i)(x−3i) B: (x+3)(x+3) A: x=3 or x=−3 A: x=3i or x=−3i A: x=3 A: x=−3i
Mathematics
1 answer:
Paraphin [41]3 years ago
5 0

Answer:

A. The solutions are x=3i,\:x=-3i.

B. The factored form of the quadratic expression x^2+9=(x-3i)(x+3i)

Step-by-step explanation:

A. To find the solutions to the quadratic equation x^2+9=0 you must:

\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}

x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i

The solutions are:

x=3i,\:x=-3i

B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.

To factor x^2+9:

First, multiply the constant in the polynomial by i^2 where i^2 is equal to -1.

x^2+9i^2

Since both terms are perfect squares, factor using the difference of squares formula

a^2-i^2=(a+i)(a-i)

x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)

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