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 compl…

Question

asked Aug 14, 2022 171k views

1 Answer

Akshay Chopra · Answer 1 · 2022-08-19T11:29:51+0000

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

#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