Question

Find the zeroes of the quadratic polynomial
f(x) = x^2/a+b/ac×(-x)/b-1/c

Answer 1

abx^2 + b^2x - acx - bc

bx(ax + b) - c(ax + b)

(ax + b)(bx - c)

so,

x = -b/a , c/b

so,

SUM OF ZEROES

-b/a+c/b = -(b^2 - ac)/ab

(-b^2 + ac)/ab = (-b^2+ac)/ab

PRODUCT OF ZEROES

(-b/a)(c/b) = -bc/ab

-bc/ab = -bc/ab

hence proved