Question

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

Answer 1

@lgbasallote

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

slope of AC * slope of BC= -1

Answer 6

so alpha* beta = -c^2

Answer 7

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

Answer 8

so ac=-1

Answer 9

does it make sense?

Answer 10

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

Answer 11

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

Answer 12

No one tags mathslover though :P

Answer 13

since when does c=(0,beta)?

Answer 14

so slope of AC= - c/alpha=m1 , slope of BC= -c/beta=m2
m1 *m2= -1...since AC is perpendicular to BC.

Answer 15

sorry C=(0,c)

Answer 16

right

Answer 17

@akash123 @ganeshie8

Answer 18

u got it?

Answer 19

yah