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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    @freckles

  2. campbell_st
    • one year ago
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    real and equal means the discriminant is zero and the discriminant is found using \[\Delta = b^2 - 4ac\]

  3. campbell_st
    • one year ago
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    you have a = (k + 5) b = -(2k + 3) c = (k + 1) so substitute the values then you can solve for k hope it helps

  4. anonymous
    • one year ago
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    4k^2+9+12k-4k^2 - 20 = 0 ?

  5. campbell_st
    • one year ago
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    so you have \[[-(2k + 3)]^2 - 4\times (k + 5) \times (k + 1)] = 0\]

  6. anonymous
    • one year ago
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    4k^2+9+12k-4k^2 - 20 = 0 ?

  7. campbell_st
    • one year ago
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    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

  8. anonymous
    • one year ago
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    4k^2 - 24k -20????? How???

  9. campbell_st
    • one year ago
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    ac: (k + 5)(k + 1) = k^2 + 6k + 5 4ac = 4k^2 + 24k + 20 does that make sense..?

  10. anonymous
    • one year ago
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    No

  11. campbell_st
    • one year ago
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    so in the equation are you happy that a = (k + 5) and c = (k + 1)...?

  12. campbell_st
    • one year ago
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    so if you multiply a and c (k + 5)(k + 1) = k^2 + 6k + 5 does that make sense..?

  13. anonymous
    • one year ago
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    Yes

  14. campbell_st
    • one year ago
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    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

  15. anonymous
    • one year ago
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    Now?

  16. campbell_st
    • one year ago
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    solve for k... -12k = 11 etc

  17. anonymous
    • one year ago
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    k = 11/12

  18. anonymous
    • one year ago
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    0.92?

  19. campbell_st
    • one year ago
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    well if -12k = 11 k = - 11/12 I'd leave it as a fraction.

  20. anonymous
    • one year ago
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    - 11/12?? It should be +???

  21. campbell_st
    • one year ago
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    is that the answer you have been provided..?

  22. anonymous
    • one year ago
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    I have no options.............

  23. campbell_st
    • one year ago
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    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

  24. anonymous
    • one year ago
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    Thanks.

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