Question

Activity 2: Directions: Determine the nature of the roots of the following quadratic equations using the discriminant. You are provided with a space 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