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

\[x^2 + 8x + 12 = 0\]

A. no real solution
B. one real solution
C. two rational solutions
D. two irrational solutions

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"> a x 2 + b x + c = 0 ⇒ Δ = b 2 − 4 ⋅ a ⋅ c Δ > 0 ⇒ tw o re a l so l u t i o n s Δ = 0 ⇒ o n e re a l so l u t i o n Δ < 0 ⇒ n o so l u t i o n − − − − − − − − − − − − − − − x 2 + 8 x + 12 = 0 ⇒ Δ = 8 2 − 4 ⋅ 1 ⋅ 12 = 64 − 48 = 16 Δ > 0 ⇒ tw o re a l so l u t i o n s ⇒ A n s . C

Answered by kate200468 | 2024-06-24

0 \\ \\ Answer : \ C. \ \ two \ rational \ solutions"> x 2 + 8 x + 12 = 0 a = 1 , b = 8 , c = 12 Δ = b 2 − 4 a c = 8 2 − 4 ⋅ 1 ⋅ 12 = 64 − 48 = 16 Δ > 0 A n s w er : C . tw o r a t i o na l so l u t i o n s

Answered by Lilith | 2024-06-24

The quadratic equation x 2 + 8 x + 12 = 0 has a discriminant of 16 , which is greater than zero, indicating it has two distinct real solutions. Therefore, the equation has two rational solutions. The correct answer is C.
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Answered by kate200468 | 2024-10-02