Polynomials MCQs

1. The number of real zeros of given polynomial is/are?

$3$
$2$
$0$
None of above

2. : The number of real zeros of given polynomial is/are?

$0$
$2$
$5$
$3$

3. Find the Quadretic given that sum ad product of its roots are $\sqrt{2}$ and $\displaystyle \frac{1}{3}$ Respectively?

$3x^2-3+1$
$3x^2-\sqrt{2}+1$
$3x^2-3\sqrt{2}+1$
None of above

4. Find the remainder when $x^3-3x^2+3x+5$ is divided by $x-2$?

$7$
$6$
$0$
None of above

5. Find the remainder when $x^3+x^2+x+1$ is divided by $x+1$ ?

$0$
$1$
$2$
None of above

6. If one root of the polynomial $f(x) = 5x^2 + 13x + k$ is reciprocal of the other , then the value of $k$ is ?

$0$
$6$
$\displaystyle \frac{1}{6}$
$5$

7. What is division algorithim for polynomails says

$p(x)=q(x)h(x)+r(x)$
$p(x)=q(x)h(x)-r(x)$
$p(x)=q(x)-h(x)r(x)$
$p(x)=q(x)+h(x)+r(x)$

8. The zeroes of the polynomial $4\sqrt{3}x^2 + 5 x - 2\sqrt{3}$ are ?

$\displaystyle \frac{\sqrt{3}}{4}, \frac{2}{\sqrt{3}}$
$\displaystyle \frac{-\sqrt{3}}{4}, \frac{2}{\sqrt{3}}$
$\displaystyle \frac{\sqrt{3}}{4}, \frac{-2}{\sqrt{3}}$
$\displaystyle \frac{-\sqrt{3}}{4}, \frac{-2}{\sqrt{3}}$

9. What is the relationship between the roots and cofficients of $3x^2-x-4$ ?

$\displaystyle \alpha .\beta =\frac{-4}{3},\alpha +\beta =\frac{-1}{3}$
$\displaystyle \alpha .\beta =\frac{4}{3},\alpha +\beta =\frac{-1}{3}$
$\displaystyle \alpha .\beta =\frac{4}{3},\alpha +\beta =\frac{1}{3}$
$\displaystyle \alpha .\beta =\frac{-4}{3},\alpha +\beta =\frac{1}{3}$

10. Is $x^2=x^2+4$ is a quadratic?

No
Yes