(Synchronous) Solving Quadratic Equations

(Synchronous) Solving Quadratic Equations

Flow of the lesson

• Timed quiz on Completing the Square, Nature of Roots and Sum & Product of Roots

• Discussion on Some items

• Questions/Clarifications

Multiple Choice

What is the next step in solving this quadratic equation using completing the square.

 $x^2+14x=32$  

•  $x^2+14x+\left(14^2\right)=32$ 
  

•  $x^2+\left(\frac{14}{2}\right)x=32$  

•  $x^2+\left(14\right)^2x=32$  

•  $x^2+14x=\frac{32}{x}$  

Multiple Choice

What is the next step in solving this quadratic equation using completing the square.

 $x^2+14x=32$  

•  $x^2+14x=32+\frac{14}{2}$ 
  

•  $x^2+14x+196=32+196$  

•  $x^2+14x+196=32$  

•  $x^2+14x+49=32+49$  

Multiple Choice

What is the next step in solving this quadratic equation using completing the square.

 $x^2+14x+49=32+49$  

•  $\left(x^2+7\right)^2=81$ 
  

•  $\left(x+7\right)^2=81$  

•  $\left(x^2+14x+7\right)^2=81$  

•  $\left(x+14\right)^2=81$  

Multiple Choice

What is the answer when you solve this quadratic equation using completing the square.

 $x^2+14x=32$  

•  $x=-16,-2$ 
  

•  $x=16,2$  

•  $x=-16,2$  

•  $x=-2,16$  

Multiple Choice

Complete the square

 $x^2-12x+$  _____

• - 36
  

• 36

• - 24
  

• 24

Multiple Choice

Solve by completing the square.

 $x^2+8x+2=0$  

•  $x=8\pm\sqrt{15}$  
  

•  $x=-8\pm\sqrt{15}$  

•  $x=4\pm\sqrt{14}$  

•  $x=-4\pm\sqrt{14}$  

ANSWER KEY

Multiple Choice

Solve by completing the square.

 $x^2-2x-12=0$  

•  $x=1\pm\sqrt{13}$  
  

•  $x=-1\pm\sqrt{13}$  

•  $x=2\pm\sqrt{15}$  

•  $x=-2\pm\sqrt{15}$  

ANSWER KEY

Multiple Choice

What is the nature of the roots when the discriminant is greater than zero and is not a perfect square.

• real, rational and unequal

• real, irrational and unequal

• real, rational, equal

• imaginary, unequal

Multiple Choice

What is the nature of the roots when the discriminant is less than zero?

• real, rational and unequal

• real, irrational and unequal

• real, rational, equal

• imaginary, unequal

Multiple Choice

What is the nature of the roots when the discriminant is equal to zero?

• real, rational and unequal

• real, irrational and unequal

• real, rational, equal

• imaginary, unequal

Multiple Choice

What is the nature of the roots when the discriminant is 100?

• real, rational and unequal

• real, irrational and unequal

• real, rational, equal

• imaginary, unequal

Multiple Choice

When can we say that the quadratic equation has only one solution?

• D = 0

• D > 0

• D < 0

Multiple Choice

Use the discriminant and state whether the roots of each equation are real, rational/irrational and equal/unequal, or imaginary and unequal.

 $2x^2-4=3x$  

• D = 41 (real, rational, unequal)
  

• D = 41 (real, irrational, unequal)

• D = 0 (real, rational, equal)

• D= -41 (imaginary, unequal)
  

Multiple Choice

Use the discriminant and state whether the roots of each equation are real, rational/irrational and equal/unequal, or imaginary and unequal.

 $x^2+6x+9=0$  

• D = 36 (real, rational, unequal)
  

• D = 36 (real, irrational, unequal)

• D = 0 (real, rational, equal)

• D= -36 (imaginary, unequal)
  

Multiple Choice

Use the discriminant and state whether the roots of each equation are real, rational/irrational and equal/unequal, or imaginary and unequal.

 $x^2-x=3\left(x+7\right)$  

• D = 100 (real, rational, unequal)
  

• D = 21 (real, irrational, unequal)

• D = 0 (real, rational, equal)

• D= -50 (imaginary, unequal)
  

Multiple Choice

Find the sum and product of the roots of the given quadratic equation.

 $2x^2+9x+3=0$  

• Sum: 9
  
  Product: 3
  

• Sum:  $-\frac{9}{2}$  
  
  Product:  $\frac{3}{2}$  
  

• Sum: -9
  
  Product: 3
  

• Sum:  $\frac{9}{2}$  
  
  Product:  $\frac{3}{2}$  
  

Multiple Choice

Write the quadratic equation whose roots have the given sum and product, sum= -12 and product = 10.

• $x^2+12x-10=0$

• $x^2-12x-10=0$

• $x^2-12x+10=0$
  

• $x^2+12x+10=0$

Multiple Choice

What is the quadratic equation whose roots are -10 and -5?

• $x^2-15x+50=0$

• $x^2-5x+50=0$

• $x^2+5x-50=0$

• $x^2+15x+50=0$