Respuesta :
Answer:
[tex]x = 1 +/- \frac{i\sqrt{10} }{2}[/tex]
Step-by-step explanation:
The equation given is:
[tex]2x^2 = 4x - 7\\\\2x^2 - 4x + 7 = 0[/tex]
Using quadratic formula:
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a}[/tex]
From the question:
a = 2, b = -4, c = 7
Therefore:
[tex]x = \frac{4 +/- \sqrt{(-4)^2 - 4 * 2 * 7} }{2 * 2}\\\\x = \frac{4 +/- \sqrt{(16 - 56)} }{4}\\\\x = \frac{4 +/- \sqrt{-40} }{4}\\[/tex]
=> [tex]x = 1 +/- \frac{i\sqrt{10} }{2}[/tex]
The solution of given quadratic equation is given as [tex]x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex]
Given the quadratic equation:
[tex]2x^2 = 4x -7[/tex]
Formula for finding roots of quadratic equation [tex]ax^2 + bx + c = 0[/tex] is given by:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]
Here, we get a = 2, b = -4, and c = 7.
Thus, the roots can be found as:
[tex]x = \dfrac{4 \pm \sqrt{16 - 56}}{4} \\\\x = \dfrac{4 \pm \sqrt{-40}}{4} \\\\x = \dfrac{4 \pm 2i\sqrt{10}}{4} \\\\\\x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex]
Thus, the solution of the given quadratic equation is given as [tex]x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex].
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