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irakobra [83]
2 years ago
8

Use the quadratic formula to solve 3x^2=5x

Mathematics
1 answer:
Oksi-84 [34.3K]2 years ago
4 0

First of all, we have to set the equation in the form p(x)=0, where p(x) is a quadratic polynomial. So, we have

3x^2-5x=0

Even though using the quadratic formula for such a simple case is a little bit overkill, it is surely doable: we have

3x^2-5x=0 \iff ax^2+bx+c=0 \iff a=3,\quad b=-5,\quad c=0

And the formula for solving is

x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

So, if we plug our values, we have

x_{1,2} = \dfrac{5\pm\sqrt{25}}{6} = \dfrac{5\pm5}{6}

And thus the solutions are

x_1=0,\quad x_2 = \dfrac{10}{6}=\dfrac{5}{3}

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