Write a quadratic equation given the roots -1/3 and 5, show your work

Question

Write a quadratic equation given the roots -1/3 and 5, show your work

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Minh Khuê 6 months 2021-08-19T19:34:26+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-19T19:35:50+00:00

     \boxed{(x - a)(x - b) = 0}

    The equation above is the intercept form. Both a-term and b-term are the roots of equation.

    x =  -  \frac{1}{3}  \\ x = 5

    These are the roots of equation. Therefore we substitute a = – 1/3 and b = 5 in the equation.

    (x +  \frac{1}{3} )(x -  5) = 0

    Here we can convert the expression x+1/3 to this.

    x +  \frac{1}{3}  = 0 \\  3x + 1 = 0

    Rewrite the equation.

    (3x + 1)(x - 5) = 0

    Simplify by multiplying both expressions.

    3 {x}^{2}  - 15x + x - 5 = 0 \\ 3 {x}^{2}  - 14x  - 5 = 0

    Answer Check

    Substitute the given roots in the equation.

    3 {(5)}^{2}  - 14(5)  - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0

    3( -  \frac{1}{3} )^{2}  - 14( -  \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) +  \frac{14}{3}  - 5 = 0 \\  \frac{1}{3}  +  \frac{14}{3}  -  \frac{15}{3}  = 0 \\  \frac{15}{3}  -  \frac{15}{3}  = 0 \\ 0 = 0

    The equation is true for both roots.

    Answer

     \large \boxed {3 {x}^{2}  - 14x - 5 = 0}

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