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    I need help approaching these types of questions because it comes up A LOT

    the equation 2x² - 3x - (k+1) = 0, where k is a constant

    Q) find the set of possible values for k (4) k has no real roots
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    RDKGames
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    I'm assuming the question asks for the values of k such that the equation has distinct real roots, or equal roots.
    If so just consider the discriminant, remember  b^2-4ac>0 for distinct real roots and  b^2-4ac=0 for equal roots (single root you may think of it as). In this case, a=2, b=-3 and  c=-(k+1) .
    If this isn't the question then please say what the actual wording of the full question was.
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    (Original post by samantham999)
    I need help approaching these types of questions because it comes up A LOT

    the equation 2x² - 3x - (k+1) = 0, where k is a constant

    Q) find the set of possible values for k (4)
    As said above, we can't really determine any restrictions on k until we have more information about the roots.

    If 2 distinct real roots; then b^2-4ac>0

    If 1 repeated real root; then b^2-4ac=0

    If 0 real roots; then b^2-4ac<0

    where a=2, b=-3, c=-(k+1)
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    (Original post by B_9710)
    I'm assuming the question asks for the values of k such that the equation has distinct real roots, or equal roots.
    If so just consider the discriminant, remember  b^2-4ac>0 for distinct real roots and  b^2-4ac=0 for equal roots (single root you may think of it as). In this case, a=2, b=-3 and  c=-(k+1) .
    If this isn't the question then please say what the actual wording of the full question was.
    The question is listed above, to find values of k and it says k has no real roots.
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    (Original post by RDKGames)
    As said above, we can't really determine any restrictions on k until we have more information about the roots.

    If 2 distinct real roots; then b^2-4ac>0

    If 1 repeated real root; then b^2-4ac=0

    If 0 real roots; then b^2-4ac<0

    where a=2, b=-3, c=-(k+1)

    Sorry, I forgot to say...k has no real roots so its obviously 0 real roots but i don't really understand the above?
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    (Original post by samantham999)
    Sorry, I forgot to say...k has no real roots so its obviously 0 real roots but i don't really understand the above?
    The value of the discriminant tells us how many real roots there are, and vice versa, the amount of roots tells us conditions which must hold for the discriminant (the one's above). Then we can use it to construct an inequality in terms of k and solve it.
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    (Original post by samantham999)
    Sorry, I forgot to say...k has no real roots so its obviously 0 real roots but i don't really understand the above?
    So you're finding the values of k so that the discriminant is strictly less than 0. Do you understand this part? Do you know why this is the case?
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    (Original post by RDKGames)
    As said above, we can't really determine any restrictions on k until we have more information about the roots.

    If 2 distinct real roots; then b^2-4ac>0

    If 1 repeated real root; then b^2-4ac=0

    If 0 real roots; then b^2-4ac<0

    where a=2, b=-3, c=-(k+1)
    yeah i thought to plug them in by labelling a,b and obviously c but how do you leave your answer?
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    (Original post by samantham999)
    yeah i thought to plug them in by labelling a,b and obviously c but how do you leave your answer?
    As an inequality with k on one side and everything else on the other. The inequality is the range of values that k can take - as required by the question - in order to have no real roots.
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    (Original post by RDKGames)
    As an inequality with k on one side and everything else on the other. The inequality is the range of values that k can take - as required by the question - in order to have no real roots.
    so i did (-3)² - 4x2-(k+1)

    which leaves 9 - 8 + 4k - 4 ?

    is this step wrong?
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    (Original post by samantham999)
    so i did (-3)² - 4x2-(k+1)

    which leaves 9 - 8 + 4k - 4 ?

    is this step wrong?
    Yes.

    (-3)^2-4(2)[-(k+1)] = 9+4(2)(k+1) = 9+8k+8
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    (Original post by RDKGames)
    Yes.

    (-3)^2-4(2)[-(k+1)] = 9+4(2)(k+1) = 9+8k+8
    why is -4x2 = -8 wrong?
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    (Original post by samantham999)
    why is -4x2 = -8 wrong?
    That's right, I just don't know where you pulled the "+4k-4" from.
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    (Original post by RDKGames)
    That's right, I just don't know where you pulled the "+4k-4" from.
    silly me. now i got 9+8k-8 BUT, is it +8 because there is a negative sign infront of the bracket like this: -8-(k+1) ?

    the answer says 8k < -17

    how do you get -17? -9 -8
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    (Original post by samantham999)
    silly me. now i got 9+8k-8 BUT, is it +8 because there is a negative sign infront of the bracket like this: -8-(k+1) ?
    Sort of, it is hard to say from your specific working because you got distributed the negative weirdly, but be careful with the way you write them. The way you represented that would read as "minus 8 take away the quantity of k+1" which is not correct - it should be "minus 8 multiplied by the negative of the quantity k+1" so the negatives cancel and you get left with 8(k+1) hence +8. Just look at my working above.
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    (Original post by RDKGames)
    Sort of, it is hard to say from your specific working because you got distributed the negative weirdly, but be careful with the way you write them. The way you represented that would read as "minus 8 take away the quantity of k+1" which is not correct - it should be "minus 8 multiplied by the negative of the quantity k+1" so the negatives cancel and you get left with 8(k+1) hence +8. Just look at my working above.
    I understand. Thanks so much! yeah, i really need to take care with my negative signs tbh -8-(k+1) because - is infront of the bracket and infront of 8 it cancels because you are multiplying

    thanks! so when i get questions like this it will see whether it has real roots or not and then i choose from the formula thing you sent first?
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    (Original post by samantham999)
    I understand. Thanks so much! yeah, i really need to take care with my negative signs tbh -8-(k+1) because - is infront of the bracket and infront of 8 it cancels because you are multiplying

    thanks! so when i get questions like this it will see whether it has real roots or not and then i choose from the formula thing you sent first?
    Essentially, yeah. Though you should probably understand where those specific restrictions come from.
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    (Original post by RDKGames)
    Essentially, yeah. Though you should probably understand where those specific restrictions come from.
    I will check out exam solutions for it thanks
 
 
 
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