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

1. -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)

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

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

2 distinct real roots means that the discriminant >0, can you take it from there?
3. 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
4. (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)

(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 ??
5. (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)

(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.
6. (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)

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

has 2 distinct real roots.
Almost right, but it is for the final answer. Then you can use this completed square form to deduce the maximum value.
7. (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.
8. (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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