Given that one of the zeroes of the cubic pol | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $p(x) = ax^3 + bx^2 + cx + d$ be the cubic polynomial.Let the zeroes of the polynomial be $\alpha, \beta,$ and $\gamma$.Given that one of the

Vedclass · Accepted Answer

$\frac{c}{a}$

Vedclass · Answer

(C) Let $p(x) = ax^3 + bx^2 + cx + d$ be the cubic polynomial.Let the zeroes of the polynomial be $\alpha, \beta,$ and $\gamma$.Given that one of the zeroes is zero,let $\alpha = 0$.According to the relationship between zeroes and coefficients of a cubic polynomial,the sum of the product of zeroes taken two at a time is given by $\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a}$.Substituting $\alpha = 0$ into the equation:$(0)\beta + \beta\gamma + \gamma(0) = \frac{c}{a}$$0 + \beta\gamma + 0 = \frac{c}{a}$$\beta\gamma = \frac{c}{a}$Thus,the product of the other two zeroes is $\frac{c}{a}$.

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

Similar Questions

For each of the following,find a quadratic polynomial whose sum and product of the zeroes are $\frac{21}{8}$ and $\frac{5}{16}$ respectively. Also,find the zeroes of these polynomials by factorisation.

The zeros of $p(x) = 3x^2 - x - 4$ are $\alpha$ and $\beta$,then $\alpha^2 \beta + \alpha \beta^2 = \ldots$

Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=2, b=3, c=-5, d=0$.

Prove that $1/2, 1$ and $-2$ are the zeros of the cubic polynomial $p(x) = 2x^3 + x^2 - 5x + 2$. Also,verify the relationship between the zeros and the coefficients.

Which of the following is a cubic polynomial?

Vedclass Test Series

Exam Paper Generator

Online Exam Module