R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: MULTIPLE-CHOICE QUESTIONS (MCQ)

If $\alpha , \beta , \gamma$ be the zeros of the polynomial $2x^3+x^2-13x+6$, then $\alpha \beta \gamma$

If $\alpha , \beta , \gamma$ be the zeros of the polynomial $p\left(x\right)$ such that $\left(\alpha +\beta +\gamma \right)=3, \left(\alpha \beta +\beta \gamma +\gamma \alpha \right)=-10$ and $a\beta \gamma =-24$ then $p\left(x\right)=$ ?

If two of the zeros of the cubic polynomial $a{x}^3+b{x}^2+cx+d$ are $0$, then the third zero is

If one of the zeros of the cubic polynomial $a{x}^3+b{x}^2+cx+d$ is$0$, then the product of other two zeros are

If one of the zeros of the cubic polynomial $x^3+a{x}^2+bx+c$ is $-1$, then the product of the other two zeros is

If $\alpha , \beta$ be the zeros of the polynomial $2x^2+5x+k$ such that ${\alpha }^2+{\beta }^2+\alpha \beta =\frac{21}{4}$, then $k=$?

On dividing a polynomial $p\left(x\right)$ by a non-zero polynomial $q\left(x\right)$, let $g\left(x\right)$ be the quotient and $r\left(x\right)$ be the remainder, then $p\left(x\right)=q\left(x\right).g\left(x\right)+r\left(x\right)$, where

Which of the following is a true statement?