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VMariaS [17]
3 years ago
15

What are the roots of f(x) = x2 – 48? –48 and 48 –24 and 24 Negative 8 StartRoot 3 EndRoot and 8 StartRoot 3 EndRoot Negative 4

StartRoot 3 EndRoot and 4 StartRoot 3 EndRoot
Mathematics
2 answers:
Ivanshal [37]3 years ago
9 0

Answer:

x=4\sqrt{3},\:x=-4\sqrt{3} are the roots.

Step-by-step explanation:

x=4\sqrt{3},\:x=-4\sqrt{3}

Considering the expression

x^2\:-\:48

Solving

x^2-48=0

x^2-48+48=0+48

x^2=48

\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{48},\:x=-\sqrt{48}

Solving

x=\sqrt{48}

  = \sqrt{2^4\cdot \:3}

  \mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}

  = \sqrt{3}\sqrt{2^4}

  \mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^m}=a^{\frac{m}{n}}

  \sqrt{2^4}=2^{\frac{4}{2}}=2^2

  =2^2\sqrt{3}

  =4\sqrt{3}

So,

x=4\sqrt{3}

Similarly,

x=-\sqrt{48}=-4\sqrt{3}

Therefore, x=4\sqrt{3},\:x=-4\sqrt{3} are the roots.

Keywords: roots, expression

Learn more about roots from brainly.com/question/3731376

#learnwithBrainly

Effectus [21]3 years ago
9 0

Answer:

The solutions are  x=4\sqrt{3} an x=-4\sqrt{3}

Step-by-step explanation:

We want to find the root of the quadratic function f(x)=x^2-48

To find the roots of this function, we set f(x)=0

This implies that:

x^2-48=0

This implies that:

x^2=48

Take square root to get;

x=\pm \sqrt{48}

x=\pm4\sqrt{3}

Therefore the solutions are  x=4\sqrt{3} an x=-4\sqrt{3}

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