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apple_pi

  • 2 years ago

The parabola y=ax^2+bx+c, c≠0 meets the x-axis at A(α,0) and B(β,0) and the y-axis at C. If AC and BC are perpendicular, prove ac=-1

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  1. apple_pi
    • 2 years ago
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    @lgbasallote

  2. akash123
    • 2 years ago
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    alpha and beta are the roots of quadratic ax^2+bx+c=0

  3. akash123
    • 2 years ago
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    so alpha + beta = -b/a and alpha* beta= c/a

  4. lgbasallote
    • 2 years ago
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    sure...tag the math hater to a math problem...makes a lot of sense

  5. akash123
    • 2 years ago
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    slope of AC * slope of BC= -1

  6. akash123
    • 2 years ago
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    so alpha* beta = -c^2

  7. akash123
    • 2 years ago
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    and put this value into... alpha* beta= c/a

  8. akash123
    • 2 years ago
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    so ac=-1

  9. akash123
    • 2 years ago
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    does it make sense?

  10. apple_pi
    • 2 years ago
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    how did you get to alpha*beta=-c^2?

  11. akash123
    • 2 years ago
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    use this...slope of AC * slope of BC= -1 c=(0, beta)

  12. mathslover
    • 2 years ago
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    No one tags mathslover though :P

  13. apple_pi
    • 2 years ago
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    since when does c=(0,beta)?

  14. akash123
    • 2 years ago
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    so slope of AC= - c/alpha=m1 , slope of BC= -c/beta=m2 m1 *m2= -1...since AC is perpendicular to BC.

  15. akash123
    • 2 years ago
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    sorry C=(0,c)

  16. apple_pi
    • 2 years ago
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    right

  17. apple_pi
    • 2 years ago
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    @akash123 @ganeshie8

  18. akash123
    • 2 years ago
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    u got it?

  19. apple_pi
    • 2 years ago
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    yah

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