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Deduce the Greatest Value of -x^2 +5x - 8 watch

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    -x^2 +5x -8

    -(x^2 -5x +8)

    -[ (x- 5/2)^2 -(5/2)^2 + 8) ]

    -[ (x-5/2)^2 -25/4 + 8 ] Side work : -25/4 + 32/4 = 7/4

    -(x-5/2)^2 + 7/4

    I this correct?

    Thanks to everyone for the help.

    Also, to save posting another thread

    Given that k is not equal to -1 (the not equal to sign a line going down and 2 dashes across it)

    show that the quadratic equation

    (k+1)x^2 + 2kx + (k-1) = 0

    has 2 distinct real roots.
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    Very nearly ... -(x-5/2)^2 - 7/4.

    2 distinct real roots means that the discriminant >0, can you take it from there?
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    yeah so x= 2.5+(sqrt 7/4) or 2.5-(sqrt 7/4)

    discriminant is b^2-4ac when ax^2 + bx + c =0
    so work out what a, b and c are and find the discriminant
    if discriminant =0 the roots are the same
    if discriminant <0 the roots are imaginary
    if discriminant is >0 there are 2 real roots
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    (Original post by vc94)
    Very nearly ... -(x-5/2)^2 - 7/4.

    2 distinct real roots means that the discriminant >0, can you take it from there?
    Given that k is not equal to -1 (the not equal to sign a line going down and 2 dashes across it)

    show that the quadratic equation

    (k+1)x^2 + 2kx + (k-1) = 0

    has 2 distinct real roots.

    b^2 - 4ac

    a= k + 1

    b= 2k

    c= k - 1

    (2k)^2 - 4(k+1)(k-1) > 0 (since 2 distinct roots)

    4k^2 - 4 (k^2 - 1) > 0

    4k^2 - 4k^2 + 4 > 0

    4 > 0 ??
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    (Original post by Tempa)
    Given that k is not equal to -1 (the not equal to sign a line going down and 2 dashes across it)

    show that the quadratic equation

    (k+1)x^2 + 2kx + (k-1) = 0

    has 2 distinct real roots.

    b^2 - 4ac

    a= k + 1

    b= 2k

    c= k - 1

    (2k)^2 - 4(k+1)(k-1) > 0 (since 2 distinct roots)

    4k^2 - 4 (k^2 - 1) > 0

    4k^2 - 4k^2 + 4 > 0

    4 > 0 ??
    You have shown that the discriminant is equal to 4, which is bigger than 0, so this means the equation has 2 distinct real roots i.e. you have answered the question.
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    (Original post by Tempa)
    -x^2 +5x -8

    -(x^2 -5x +8)

    -[ (x- 5/2)^2 -(5/2)^2 + 8) ]

    -[ (x-5/2)^2 -25/4 + 8 ] Side work : -25/4 + 32/4 = 7/4

    -(x-5/2)^2 + 7/4


    I this correct?

    Thanks to everyone for the help.

    Also, to save posting another thread

    Given that k is not equal to -1 (the not equal to sign a line going down and 2 dashes across it)

    show that the quadratic equation

    (k+1)x^2 + 2kx + (k-1) = 0

    has 2 distinct real roots.
    Almost right, but it is -(x-\frac{5}{2})^2 -\frac{7}{4} for the final answer. Then you can use this completed square form to deduce the maximum value.
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    (Original post by Maths_Lover)
    You have shown that the discriminant is equal to 4, which is bigger than 0, so this means the equation has 2 distinct real roots i.e. you have answered the question.
    Lol I got this answer before when I was doing the past paper and I'm like I'm wrong so lets head to the TSR.

    Thanks anyway.
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    (Original post by Tempa)
    Lol I got this answer before when I was doing the past paper and I'm like I'm wrong so lets head to the TSR.

    Thanks anyway.
    You are welcome.
 
 
 
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