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  • Given that one of the zeroes of the cubic polynomial ax^3 + bx^2 + cx + d is zero, the product of the other two zeroes is

Given that one of the zeroes of the cubic polynomial ax^3 + bx^2 + cx + d is zero, the product of the other two zeroes is

(A) -\frac{c}{a}

(B) \frac{c}{a}

(C) 0

(D) -\frac{b}{a}

Answers (1)

Answer. [B]

Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 3.

Here the given cubic polynomial is ax^3 + bx^2 + cx + d

Let three zeroes are \alpha ,\beta ,\gamma

\alpha =0 (given)    …..(1)

we know that

\alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a}

Put \alpha =0

\beta \gamma =\frac{c}{a}           ( using equation (1))

Hence the product of other two zeroes is \frac{c}{a}.

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