CPhill

To have two roots.....the discriminant must be a perfect square > 0.....so...

5a^2 - 26a - 8  +  4 (1)(a^2 - 4a + 9)   simplify

9a^2 - 42a + 28

Graphing this...it will be  > 0   and a perfect square   when the integer value for a  = 6

So  the polynomial  is

x^2   - 4x  - 21      factor ( x - 7) ( x + 3)  and the roots are  - 3  and 7

CORRECTED

The discriminant  is

(m - 2)^2  - 4m (m - 3)

To have multiple roots....this must be a perfect square > 0

(m - 2)^2  - 4m (m - 3)  simplify

m^2 - 4m + 4 - 4m^2 + 12m

-3m^2 + 8m + 4

Graphing this.....it is only > 0   when the integer values for m  =    0, 1, 2 or 3

There are two values for m that produce a perfect square

When m  = 1.....the perfect square is 9

When m = 3, the perfect square is 1

So....one possible quadratic is

x^2 + x - 2    factoring we have (x + 2) (x - 1)  and the roots are  -2 and 1

The other possible quadratic is

3x^2  - x     factor   x (3x - 1)   and the roots are  0 and 1/3

However....we require integer roots...so

x^2 + x - 2  is the quadratic     and m = 1

Remember that  x  is the additonal dollars that she  puts in her savings account aftr she earns $200.....she contributes $20 as long as she  only makes $200

After  $200, she puts  every  dollar into the account...

So  the final amount she contributes (saves) is 20 + x

And the total amount she makes is  200 +  x

So.....the  ratio of savings / total paycheck  = [ 20 + x ] / [ 200 + x ]

Example ...suppose she eans $240 dollars

She puts $40  into the account

So.....the ratio of savings / total paycheck  =  [ 20 + 40 ] / [200 + 40 ] = 60 / 240  = .25  = 25%

No prob  !!!

Rearrange as 

sqrt  ( 2x  - 4)  = x - 6      (1)   square both sides

2x - 4  =  x^2 - 12x + 36      simplify

x^2 - 14x + 40    =  0

(x - 10)  (x - 4)    =  0

So  possible values of x =   4    or    10

  10 is good

    4 is extraneous   .... the left side  of (1) can only be 0 or positive....but 4 makes the right side negative

  [ Last answer ]

Yep....replace "row"  with "n"

Example

-2x^3

When x  is a large negagtive......y is positive

When x is a large positive.....y is negative

So

"Up" at the left end   and "Down" at the right end

So.....the third answer

Seats  in row  N  =

12  + 4 ( N - 1)

Note ...for example.... that on  row 2  we have 

 12 + 4 (2 - 1)  = 

12 + 4(2 - 1)  = 

12 + 4(1)  =

16 seats

Original ratio of saved to total money per paycheck  = 20 / 200    (10 %)

Final ratio of saved to total money per paycheck  = [ x + 20 ] / [ x + 200 ]

Final amt saved per paycheck =   x + 20

2.  The triangles are not congruent.......no angles match