Math

What does it mean when it says Roots (order) for a function eg. -x^3-2x^2+15x+36

What i mean is how do you the answer.

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  1. the highest exponent is the order...and the number of roots

    a root is a value that makes the function equal to zero

    you can test values for roots
    ... 4 works here

    divide the function by (x - 4) to factor out the known root
    ... this leaves a quadratic
    ... use the quadratic formula for the last two roots

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  2. so if i found that the roots are -3 and 4 how would i write that?

    -3(order 2), 4

    because at -3 the function acts like a quadratic but at 4 it acts linear.

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  3. -3 is not a root

    the roots are ... -3±i

    4, -3+i, -3-i

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  4. the highest exponent is the degree
    the order of a root is the number of times it appears.

    So, you have three roots of degree 1.

    Any polynomial of degree n has exactly n roots, though all may not be unique (order 1).

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