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Bingel [31]
3 years ago
9

Which are the solutions of x^2 = –11x + 4?

Mathematics
1 answer:
strojnjashka [21]3 years ago
3 0

This is a quadratic equation, i.e. an equation involving a polynomial of degree 2. To solve them, you must rearrange them first, so that all terms are on the same side, so we get

x^2 + 11x - 4 = 0

i.e. now we're looking for the roots of the polynomial. To find them, we can use the following formula:

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

where x_{1,2} is a compact way to indicate both solutions x_1 and x_2, while a,b,c are the coefficients of the quadratic equation, i.e. we consider the polynomial ax^2+bx+c.

So, in your case, we have a=1,\ \ b=11,\ \ c=-4

Plug those values into the formula to get

x_{1,2} = \frac{-11\pm\sqrt{121+16}}{2} = \frac{-11\pm\sqrt{137}}{2}

So, the two solutions are

x_1 = \frac{-11+\sqrt{137}}{2}

x_2 = \frac{-11-\sqrt{137}}{2}

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