Question

Given that two of the zeroes of the cubic polynomial ax^3+bx^3+CX+d are 0,the third zero is

Answer 1

$\bf\huge\underline{Question}$

Given that two of the zeroes of the cubic polynomial ax^3+bx^3+cx+d are 0,the third zero is

$\bf\huge\underline{Solution}$

Let p(x) = ax³ + bx² + cx + d

$let \: \alpha \: \beta \: and \: \gamma \:be \: the \: zeros \: of \: p(x)\:where$ $\alpha=0$

We know that, sum of product of zeros taken two at a time

$\frac{c}{a} = \alpha \beta + \beta \gamma + \gamma \alpha \\ = > 0 \times \beta + \beta \gamma + \gamma \times 0 = \frac{c}{a} \\ = > \beta \gamma = \frac{c}{a}$

Hence, product of other two zeroes = c/a