Solve the quadratic equation 3x – 5x – 7 = 0 Give your answers to 3 significant figures.

Question

Solve the quadratic equation 3x – 5x – 7 = 0
Give your answers to 3 significant figures.

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RI SƠ 5 years 2021-08-12T21:37:00+00:00 1 Answers 80 views 0

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  1. Gerda
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    2021-08-12T21:38:46+00:00
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    Answer:

    The solutions of 3\cdot x^{2}-5\cdot x -7 = 0 are x_{1} \approx 2.573 and x_{2} \approx -0.907.

    Step-by-step explanation:

    The statement is incomplete. The complete description will be shown below:

    Solve the quadratic equation 3\cdot x^{2}-5\cdot x -7 = 0. Give your answers to 3 significant figures.

    From Algebra we know that second order polynomials of the form a\cdot x^{2}+b\cdot x + c = 0, a \ne0 can be solved anatically by means of the Quadratic Formula, that is:

    x = \frac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a} (1)

    Where a, b, c are coefficients of the given polynomial.

    If we know that a = 3, b = -5 and c = -7, then the roots of the polynomial are:

    x_{1,2} = \frac{5\pm \sqrt{(-5)^{2}-4\cdot (3)\cdot (-7)}}{2\cdot (3)}

    x_{1,2} = \frac{5}{6}\pm \frac{\sqrt{109}}{6}

    That is,

    x_{1} \approx 2.573 and x_{2} \approx -0.907

    The solutions of 3\cdot x^{2}-5\cdot x -7 = 0 are x_{1} \approx 2.573 and x_{2} \approx -0.907.

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