Are the following statements 'True' or 'False | vedclass

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

Question

(A) True. Let the zeroes of the cubic polynomial be $\alpha, \beta,$ and $\gamma$. It is given that two of the zeroes are $0$. Let $\alpha = 0$ and $\

Vedclass · Accepted Answer

True

Vedclass · Answer

(A) True. Let the zeroes of the cubic polynomial be $\alpha, \beta,$ and $\gamma$. It is given that two of the zeroes are $0$. Let $\alpha = 0$ and $\beta = 0$.The cubic polynomial can be expressed as $f(x) = k(x - \alpha)(x - \beta)(x - \gamma)$,where $k$ is a non-zero constant.Substituting the values: $f(x) = k(x - 0)(x - 0)(x - \gamma) = k(x^2)(x - \gamma) = k(x^3 - \gamma x^2) = kx^3 - k\gamma x^2$.Comparing this with the general form $ax^3 + bx^2 + cx + d$,we see that the coefficients of the linear term $(c)$ and the constant term $(d)$ are both $0$. Thus,the polynomial does not have linear and constant terms.

Are the following statements 'True' or 'False'? Justify your answers.
If two of the zeroes of a cubic polynomial are zero,then it does not have linear and constant terms.

Similar Questions

Obtain the value of the following polynomial at the given value of $x$: $p(x) = 2x^4 - x^2 + 5x - 8$ at $x = -3$.

Find the zeros of the following quadratic polynomial: $15x^2 + 16x + 4$.

The graph of $p(x) = x^2 - 9$ intersects the $X$-axis in .......... distinct points.

Divide $3 x^{4}+5 x^{3}-7 x^{2}+2 x+2$ by $x^{2}+3 x+1$.

The zero of $p(x) = -x^2 + 2x - 1$ is..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Are the following statements 'True' or 'False'? Justify your answers.If two of the zeroes of a cubic polynomial are zero,then it does not have linear and constant terms.