Find the zeroes of the quadratic polynomial f(x) = abx2 + (b2 – ac)x – bc.

Question

Philoid · Accepted Answer

Zeroes of polynomial means for what value of x the equation becomes 0

f(x) = abx² + (b² – ac)x – bc

⇒ f(x) = 0

⇒ abx² + (b² – ac)x – bc = 0

⇒ abx² + b²x – acx – bc = 0

⇒ bx(ax + b) – c(ax + b) = 0

⇒ (bx – c)(ax + b) = 0

⇒ bx – c = 0 and ax + b = 0

⇒ bx = c and ax = –b

Hence zeroes of polynomial f(x) are and

Find the zeroes of the quadratic polynomial f(x) = abx² + (b² – ac)x – bc.