Question

find the zeroes of cubic polynomial x²-5x²+6x without drawing the graph of the polynomial
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Answer 1

Answer:

2 and 3

Explanation:

x²-5x²+6x

$x ^{3} -5x²+6x \\ = x( {x}^{2} - 5x + 6) \\ = x( {x}^{2} - 2x - 3x + 6 )$

= x[ x ( x - 2 ) - 3 ( x-2 ) ]

$x(x - 2)(x - 3)$

$x(x - 2)(x - 3) = 0 \\ x = 0 \: or \: x - 2 = 0 \: or \: x - 3 = 0 \\ x = 0 \: or \: x = 2 \: or \: x = 3$