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solve for the roots in simplest form using the quadratic formula 4x^2-12x=-17

Sagot :

sqdancefan

9514 1404 393

Answer:

  x = 3/2 ± i√2

Step-by-step explanation:

For quadratic ax² +bx +c = 0, the roots are given by the formula ...

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

When we put your equation into standard form:

  4x^2 -12x +17 = 0

we see the relevant formula values are ...

  a = 4, b = -12, c = 17

Then the roots are ...

  [tex]x=\dfrac{-(-12)\pm\sqrt{(-12)^2-4(4)(17)}}{2(4)}=\dfrac{12\pm\sqrt{-128}}{8}\\\\x=\dfrac{3\pm2\sqrt{2}i}{2}=\boxed{\dfrac{3}{2}\pm i\sqrt{2}}[/tex]

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