Q1 Math Quiz Day 3 of 5

What are the values of a, b, and c in the equation

 $2x\left(x-2\right)=1$  so that we can solve the equation by using the quadratic formula? (1 min)

•  $a=2,\ b=4,\ c=1$  

•  $a=2,\ b=-4,\ c=1$  

•  $a=2,\ b=-4,\ c=1$  

•  $a=2,\ b=-4,\ c=-1$  

Which of the following is the correct solution in solving for x by using the quadratic formula in the equation

 $3x^2-5x-1=0?$  2 min

•  $x=\frac{5\pm\sqrt{5^2-4\left(3\right)\left(-1\right)}}{2\left(3\right)}$  

•  $x=\frac{-5\pm\sqrt{\left(-5\right)^2-4\left(3\right)\left(1\right)}}{2\left(3\right)}$  

•  $x=\frac{-5\pm\sqrt{\left(-5\right)^2-4\left(3\right)\left(-1\right)}}{2}$  

•  $x=\frac{5\pm\sqrt{\left(-5\right)^2-4\left(3\right)\left(-1\right)}}{6}$  

What are the roots of the quadratic equation

 $x^2+4x+2=0?$  (3 min)

•  $2\pm\sqrt{2}$  

•  $-2\pm\sqrt{2}$  

•  $\frac{2\pm\sqrt{8}}{2}$  

•  $\frac{-2\pm\sqrt{8}}{2}$  

The solutions to the equation

 $x^2=2x-5$  are  (3 min)

•  $x=1-2i\ or\ x=1+2i$  

•  $x=-3\ or\ x=1$  

•  $x=-1-2i\ \ or\ \ x=-1+2i$  

•  $x=-1\ \ or\ \ x=3$  

What is the discriminant of the quadratic equation

 $4x^2+2x-1=0$  ? (2 min)

•  $\sqrt{20}$  

•  $\sqrt{-12}$  

•  $20$  

•  $-12$  

What is the nature of the roots of the quadratic equation

 $6x+1=-9x^2$  ?  (2 min)

• 2 distinct real roots

• 1 real root

• 2 distinct nonreal or imaginary roots

• can not be determined

Which of the following equations have 2 distinct real roots? (3 min)

I.   $x^2+x+1=0$  

II.   $x^2-x-1=0$  

III.   $x^2-x+1=0$  

IV.   $x^2+x-1=0$  

• I & III only

• II & IV only

• I & II only

• III & IV only

Which of the following in NOT TRUE when the equation 

 $2x^2-3x-2=0$  is solved by using the quadratic formula? (3 min)

• The discriminant is a perfect square.

•  $x=\frac{-\left(-3\right)\pm\sqrt{-3^2-4\left(2\right)\left(-2\right)}}{2\left(3\right)}$  

• The equation has 2 distinct real root.

• The solutions are  $-\frac{1}{2}\ \&\ 2.$  

Which of the following equations is correct when  we are solving quadratic equations by the quadratic formula? (1 min)

•  $D=4ac-b^2$  

•  $x=\frac{-b\ \ \sqrt{b^2-4ac}}{2a}$  

•  $x=\frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$  

•  $D=\frac{b^2-4ac}{2a}$  

What must be the first step in solving the equation

 $2x-3=-6x^2$  by using the quadratic formula? (1 min)

• Divide both sides by  $-6.$  

• Add  $6x^2$  to both sides of the equation.

• Subtract  $6x^2$  to both sides of the equation.

• Determine the values of a, b, and c.