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Diana.xL

  • one year ago

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  1. Diana.xL
    • one year ago
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    Find the value of the discriminant for each quadratic equation below. Show all steps needed to write the answer in simplest form, including substituting the values of a, b, and c in the discriminant formula. Then use the value to determine how many real number solutions each equation has. 5x^2 + x = 4

  2. misty1212
    • one year ago
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    HI!!

  3. Diana.xL
    • one year ago
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    Hey :)

  4. misty1212
    • one year ago
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    start by setting it equal to zero go from \[5x^2 + x = 4\] to \[5x^2+x-4=0\]

  5. misty1212
    • one year ago
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    \[\large \color{red}ax^2+\color{blue}bx+\color{green}c=0\] \[\huge \color{red}5x^2+\color{blue}1x+\color{green}{-4}=0\]

  6. misty1212
    • one year ago
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    then as @risn said compute \[\huge \color{blue}b^2-4\times \color{red}a\times \color{green}c\]

  7. Diana.xL
    • one year ago
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    D= 1 - 4 (1)(-4)?

  8. misty1212
    • one year ago
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    nope

  9. misty1212
    • one year ago
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    \(\color{red}a=\color{red}{5}\)

  10. Diana.xL
    • one year ago
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    oh sorry. D = 1-4(5)(-4)

  11. misty1212
    • one year ago
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    yeah that is right what do you get?

  12. Diana.xL
    • one year ago
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    81?

  13. Diana.xL
    • one year ago
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    as my final answer?

  14. misty1212
    • one year ago
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    yeah me too

  15. Diana.xL
    • one year ago
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    at the end of the question it asks us "Then use the value to determine how many real number solutions each equation has".

  16. misty1212
    • one year ago
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    that is the answer to Show all steps needed to write the answer in simplest form, including substituting the values of a, b, and c in the discriminant formula.

  17. misty1212
    • one year ago
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    ok two steps here 81 is positive, so there are two real solutions also 81 is a "perfect square" it is the square of 9 that means both solutions are rational numbers

  18. Diana.xL
    • one year ago
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    oh ok! thank u so much! :)

  19. misty1212
    • one year ago
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    in fact that means \[5x^2+x-4=0\] can be solved by factoring you get \[(5x-4)(x+1)=0\] so \[x=\frac{4}{5}\] or \[x=-1\]

  20. misty1212
    • one year ago
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    \[\color\magenta\heartsuit\]

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