Question

Activity 1: Directions: Use the values of a, b and c of each of the following quadratic equations in finding the sum and the product of its roots. By inspection or by any appropriate method, determine the roots. Use the space provided for your solutions and complete the table below.​

Answer 1

`\\ \sf\longmapsto D=b^2-4ac`

#1

`\\ \sf\longmapsto x^2+6x+9=0`

Now

`\\ \sf\longmapsto D=(6)^2-4(1)(9)=36-36=0`

• Roots are real and equal

#2

`\\ \sf\longmapsto x^2+9x+20=0`

Now

`\\ \sf\longmapsto D=(9)^2-4(1)(20)=81-80=1`

• Roots are real and rational

#3

`\\ \sf\longmapsto x^2+6x+3=0`

Now

`\\ \sf\longmapsto D=6^2-4(1)(3)=36-12=24`

• Roots are real and distinct and irrational.

#4

`\\ \sf\longmapsto 2x^2-10x+8=0`

Now

`\\ \sf\longmapsto D=(-10)^2-4(1)(8)=100-32=68`

• Roots are real and distinct and irrational.

#5

• x^2+5x+10=0

Now

`\\ \sf\longmapsto D=5^2-4(1)(10)=25-40=-15`

• Roots are not real.

#6

• x^2-3x+1=0

`\\ \sf\longmapsto D=(-3)^2-4(1)(1)=9-4=5`

• Roots are real and distinct and irrational