## apple_pi 3 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

1. apple_pi

@lgbasallote

2. akash123

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

3. akash123

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

4. lgbasallote

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

5. akash123

slope of AC * slope of BC= -1

6. akash123

so alpha* beta = -c^2

7. akash123

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

8. akash123

so ac=-1

9. akash123

does it make sense?

10. apple_pi

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

11. akash123

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

12. mathslover

No one tags mathslover though :P

13. apple_pi

since when does c=(0,beta)?

14. akash123

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

15. akash123

sorry C=(0,c)

16. apple_pi

right

17. apple_pi

@akash123 @ganeshie8

18. akash123

u got it?

19. apple_pi

yah