Simplifying Polynomials Quiz 1

Question 1

If l and m are the roots of the polynomial $$g(x)=3{{x}^{2}}-12x+6$$, then find the value of $$\dfrac{1}{{{l}^{2}}}+\dfrac{1}{{{m}^{2}}}-lm$$.

Accepted Answer

1

Answer

2

Answer

-1

Answer

-2

Question 2

If $$x-\dfrac{1}{2}$$ is a factor of $$f(x)=2{{x}^{3}}-7{{x}^{2}}+ax-6$$, then find the value of $$a$$.

Accepted Answer

$$15$$

Answer

$$-2$$

Answer

$$\dfrac{1}{5}$$

Answer

$$-5$$

Question 3

Solve for $$x: 3{{x}^{2}}-(5+16i)x+25i-5=0$$.

Accepted Answer

$$x=5i,\dfrac{5+i}{3}$$

Answer

$$x=5i,-5i$$

Answer

$$x=-5i,\dfrac{5+i}{3}$$

Answer

$$x=\dfrac{5+i}{4},\dfrac{5-i}{4}$$

Question 4

If the zeros of the polynomial $$p(y)={{y}^{3}}-24{{y}^{2}}+188y+k$$ are positive consecutive even numbers, then find the value of $$k$$.

Accepted Answer

-480

Answer

460

Answer

400

Answer

-320

Question 5

If $$f$$ and $$g$$ are the zeros of $$p(x)={{x}^{2}}-cx+d-1$$, then which of the following conditions is true?

Accepted Answer

$$({{f}^{2}}-1)({{g}^{2}}-1)={{d}^{2}}-{{c}^{2}}$$

Answer

$$(1+f)(1+g)=c-d$$

Answer

$$(1-f)(1-g)=c+d$$

Answer

$$(1+{{f}^{2}})(1+{{g}^{2}})={{(c-d)}^{2}}$$