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Maths question finding what k is?

I am having difficulty answering this question, I am in the beginning of my as maths course and I have been asked this question, I don't know how to solve it or what the answer is, please help:

Given that the discriminant, b^2 - 4ac, of the quadratic f(x) = x^2 - kx - k + 1 is -7, find the possible values of k.

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  • 9 years ago
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    k = -3 or -1

    For the general quadratic ax^2 + bx +c = f(x), "solving" means finding the roots of the equation.

    And the roots occur where the graph cuts the x -axis.

    And at that point, the y-co-ordinate = 0

    Now since y and f(x) are identical in meaning (that's why y = f(x)) we can write our quadratic as

    ax^2 +bx +c = 0

    As you probably know, the roots are found by

    x = {-b +/-rt[b^2 - 4ac]} / 2a

    The term under the square root sign is called the Discriminant, because it tells you what kind of roots you are going to get.

    If b^2-4ac is positive, you can take its square root, then add that and subtract that to -b to get 2

    numbers to be divided by 2a. Hence 2 answers so 2 unequal roots in the Real Number System

    Mathmeticians are fond of shortening this sentence to "2 Real unequal roots"

    If b^2 -4ac is 0, then two Real identical roots. Sometimes people say "one Real root",since the square root of 0 is 0, and {-b+/-0}/2a is -b/2a. This looks like one answer, but that conflicts with the

    Fundamental Theorem of Algebra, which says every polynomial has as many roots as the highest

    exponent in the polynomial.

    So we say "2 roots, both equal", or "2 Real equal roots". This satisfies everybody.

    If b^2 - 4ac is negative then there still exists 2 roots, but they won't be found in the Real Numbers System. We're into Complex Numbers System

    Now, on to your question

    x^2 -kx -k+1 has a Discriminant of -7

    Comparing this to ax^2 + bx +c =0

    a = 1, b=-k, c = -k+1

    So b^2 -4ac is (-k)^2 -4(1)(-k+1) and this equals -7

    k^2 +4k -4 = -7

    k^2+4k -4+7 = 0

    k^2 + 4k +3 = 0

    (k+3)(k+1) = 0

    Now for (k+3)(k+1) to multiply out to give 0,

    Either k+3=0 or k+1 =0

    In which case k = -3 or -1

    Pardon the long comments. I felt that if you are just at the beginning of your as math as course you

    might like a detailed discussion about the Discriminant

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