Q. 44.0( 21 Votes )

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Answer :

t3 - 2t - 15t = 0


Taking t common


t (t2 - 2t - 15) = 0


By splitting the middle term


t {t2 - (- 3t + 5t) - 15} = 0


t (t2 + 3t - 5t - 15) = 0


t {t(t + 3) - 5(t + 3)} = 0


t (t + 3)(t - 5) = 0


t = - 3, 0, 5


Verification:


Sum of the zeroes = - (coefficient of x2) ÷ coefficient of x3


α + β + γ = - b/a


(0) + (- 3) + (5) = - (- 2)/1


= 2 = 2


Sum of the products of two zeroes at a time = coefficient of x ÷ coefficient of x3


αβ + βγ + αγ = c/a


(0)(- 3) + (- 3) (5) + (0) (5) = - 15/1


= - 15 = - 15


Product of all the zeroes = - (constant term) ÷ coefficient of x3


αβγ = - d/a


(0)(- 3)(5) = 0


0 = 0


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