Question

(k+5)x^2 - (2k + 3)x + (k + 1) = 0
The roots are real and equal

Answer 1

@freckles

Answer 2

real and equal means the discriminant is zero

and the discriminant is found using

\[\Delta = b^2 - 4ac\]

Answer 3

you have

a = (k + 5)

b = -(2k + 3)

c = (k + 1)

so substitute the values then you can solve for k

hope it helps

Answer 4

4k^2+9+12k-4k^2 - 20 = 0 ?

Answer 5

so you have

\[[-(2k + 3)]^2 - 4\times (k + 5) \times (k + 1)] = 0\]

Answer 6

4k^2+9+12k-4k^2 - 20 = 0 ?

Answer 7

well the 1st part is ok...

b^2 = 4k^2 + 12k + 9

4ac = 4(k^2 + 6k + 5)

then

b^2 - 4ac : 4k^2 + 12k + 9 - 4k^2 - 24k -20 = 0

so collect like terms and solve for k

Answer 8

4k^2 - 24k -20?????
How???

Answer 9

ac: (k + 5)(k + 1) = k^2 + 6k + 5

4ac = 4k^2 + 24k + 20

does that make sense..?

Answer 10

No

Answer 11

so in the equation are you happy that

a = (k + 5) and c = (k + 1)...?

Answer 12

so if you multiply a and c

(k + 5)(k + 1) = k^2 + 6k + 5

does that make sense..?

Answer 13

Yes

Answer 14

so then 4ac = 4k^2 + 24k + 20

so b^2 - 4ac is

4k^2 + 12k + 9 - 4k^2 -24k - 20 = 0

collect like terms

-12k - 11 = 0

Answer 15

Now?

Answer 16

solve for k...

-12k = 11

etc

Answer 17

k = 11/12

Answer 18

0.92?

Answer 19

well if -12k = 11

k = - 11/12

I'd leave it as a fraction.

Answer 20

- 11/12??
It should be +???

Answer 21

is that the answer you have been provided..?

Answer 22

I have no options.............

Answer 23

well are you happy that after collecting like terms

-12k - 11 = 0

then you can multiply every term by -1

and get

12k + 11 = 0

and then you still get

12k = -11

so

k = -11/12

Answer 24

Thanks.