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



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apple_pi
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@lgbasallote

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

akash123
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so alpha + beta = b/a and alpha* beta= c/a

lgbasallote
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sure...tag the math hater to a math problem...makes a lot of sense

akash123
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slope of AC * slope of BC= 1

akash123
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so alpha* beta = c^2

akash123
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and put this value into... alpha* beta= c/a

akash123
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so ac=1

akash123
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does it make sense?

apple_pi
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how did you get to alpha*beta=c^2?

akash123
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use this...slope of AC * slope of BC= 1
c=(0, beta)

mathslover
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No one tags mathslover though :P

apple_pi
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since when does c=(0,beta)?

akash123
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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.

akash123
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sorry C=(0,c)

apple_pi
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right

apple_pi
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@akash123 @ganeshie8

akash123
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u got it?

apple_pi
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yah