Question

Use the discriminant to determine the number and type of solutions the equation has.

x2 + 8x + 12 = 0
a. no real solution
b. one real solution
c. two rational solutions
d. two irrational solutions

Please help me :)

Answer 1

`ax^2+bx+c=0\ \ \ \Rightarrow\ \ \ \Delta=b^2-4\cdot a\cdot c\\\\\Delta>0\ \ \ \Rightarrow\ \ \ two\ real\ solutions\\\Delta=0\ \ \ \Rightarrow\ \ \ one\ real\ solution\\\Delta<0\ \ \ \Rightarrow\ \ \ no\ solution\\---------------\\x^2+8x+12=0\ \ \ \ \Rightarrow\ \ \ \Delta=8^2-4\cdot 1\cdot12=64-48=16\\\\\Delta>0\ \ \ \ \Rightarrow\ \ \ two\ real\ solutions\ \ \ \Rightarrow\ \ \ Ans.\ C`

Answer 2

`x^2 + 8x + 12 = 0\\ \\a=1 , b= 8, c= 12 \\ \\ \Delta =b^2-4ac = 8^2 -4\cdot1\cdot12= 64-48= 16\\ \\\Delta > 0 \\ \\ Answer : \ C. \ \ two \ rational \ solutions`