Fundamental Theorem of Algebra

Q.

Let $\mathrm{a}$ be an integer such that all the real roots of the polynomial $2{\mathrm{x}}^5+5{\mathrm{x}}^4+10{\mathrm{x}}^3+10{\mathrm{x}}^2$ $+10\mathrm{x}+10$ lie in the interval $(\mathrm{a},\mathrm{a}+1)$. Then, $\left|\mathrm{a}\right|$is equal to

Q. The sum of all non-integer roots of the equation $x^5–6x^4+11x^3–5x^2–3x+2=0$ is

1. -11
2. 3
3. -5
4. 6

Q. Fundamental theorem of algebra states that a polynomial equation of $n$ degree have exactly $n$ roots, either real or imaginary.

1. True
2. False

Q. The degree of the polynomial function \(f(x)=(x-1)^2(x+2)^2\) is \(4.\)

Q. The total possible no. of roots of the equation $4x^7+3x^6+2x^5+9x^4+4x^3+x^2+9x+9=0$ is

Q. If the equation $x^3-8x^2+cx+d=0\forall c,d\in R$ has one complex root and one positive root, then select the correct statement.

1. $c<0,d>0$
2. $c>0,d<0$
3. $c<0,d<0$
4. $c,d>0$