Answered

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If a number is subtracted from three times its square, the result is four. Find all such numbers.

Sagot :

BrotherGoku

Answer:

4/3

-1

Step-by-step explanation:

Consider that number as x, the condition is represented by the equation

[tex]3x^2-x = 4[/tex]

where x is the number, subtracted by 3x^2, which gives 4.

With this, all you need to do is solve for x by quadratic.

[tex]3x^2-x = 4\\3x^2-x-4 = 0\\x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]a = 3 \\b= -1\\x = -4[/tex]

[tex]x = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-4)}}{2(3)}[/tex]

[tex]x = \frac{1\pm\sqrt{1+48}}{6}[/tex]

[tex]x = \frac{1\pm\sqrt{49}}{6}[/tex]

[tex]x = \frac{1\pm7}{6}[/tex]

[tex]x_1 = \frac{8}{6} = 4/3\\x_2 = \frac{-6}{6} = -1[/tex]

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