Question

Find the zeroes of the quadratic polynomial

1) x^2/a + b/ac * - x/b- 1/c

Answer 1

Answer:

To find the zeros of the quadratic polynomial we will equate f(x) to 0

∴f(x)=0⇒43‾√x2+5x−23‾√=0⇒43‾√x2+8x−3x−23‾√=0⇒4x(3‾√x+2)−3‾√(3‾√x+2)=0

⇒(3‾√x+2)(4x−3‾√)=0⇒(3‾√x+2)=0 or (4x−3‾√)=0⇒x=−23√ or x=3√4

Hence, the zeros of the quadratic polynomial f(x)=43‾√x2+5x−23‾√ are −23√ or 3√4.

Answer 2

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