Quadratics — Quiz 5

Questions in this quiz (7)

1. For what integer $$k$$ are both solutions of the equation $$x^2+kx+16=0$$ negative integers?

   • $$-8$$
   • $$-17$$
   • $$10$$
   • $$16$$

2. In the quadratic expression $$bx^2+160x+d$$, $$b$$ and $$d$$ are positive constants. If $$px+q$$ is a factor of the expression, where $$p$$ and $$q$$ are positive constants, what is the greatest possible value of $$bd$$?

   • $$6400$$
   • $$160$$
   • $$240$$
   • $$800$$

3. The given quadratic function $$36x^4+151x^2+140$$ has factors in the form $$(k)(ax^2+b)(cx^2+d)$$. If $$a,b,c,d$$ and $$k$$ are integers, what is the smallest possible value of $$ab$$?

   • $$7$$
   • $$10$$
   • $$20$$
   • $$28$$

4. If $$b - 4\sqrt{b} - 12 = 0$$ and $$b$$ is a real number, what is the value of $$b$$?

   • $$36$$
   • $$36 , 4$$
   • $$6 , -2$$
   • $$36 , 4$$

5. Given the equation $$(x-9)(x-a)=x^2-4ax+b$$, where $$a$$ and $$b$$ are constants, and the equation is true for all values of $$x$$, what is the value of $$b$$?

   • 3
   • 27
   • 9
   • 4

6. Solve the equation by using the formula:$$\frac{1}{x-2}+\frac{1}{x-3}+\frac{1}{x-4}=0$$

   • $$-3, \sqrt{3}$$
   • $$\pm\frac{\sqrt{3}}{2}$$
   • $$-3, 3$$
   • $$3\pm\frac{\sqrt{3}}{3}$$

7. If one root of the equation $$x^2+ax+8=0$$ is $$4$$ while the equation $$x^2+ax+b=0$$ has equal roots, find $$b$$.

   • 9
   • 36
   • 4
   • 2