Which of the following equations has only one solution? A)x^2+4x+4=0; B)x^2+x=0;C)x^2-1

Rishi Alvarado

Rishi Alvarado

Answered question

2023-01-20

Which of the following equations has only one solution?
A)x2+4x+4=0
B)x2+x=0
C)x2-1

Answer & Explanation

Elizabeth Oneill

Elizabeth Oneill

Beginner2023-01-21Added 6 answers

The true option is A x2+4x+4=0
Justification of the ideal selection:
Options (A)
Factorize the equation x2+4x+4=0 by splitting the middle term.
x2+4x+4=0x2+2x+2x+4=0Writethemiddleterm4xas2x+2xxx+2+2x+2=0x+2x+2=0x+22=0x+2=0Ifx2=0,thenx=0x+2-2=0-2Subtract2frombothsidesoftheequationx=-2
Thus, x2+4x+4=0 has one root x=-2.
Hence, options (A) have one root.
Explanation for incorrect answer:
Options (B):
Factorize the equation x2+x=0 .
x2+x=0xx+1=0x=0orx+1=0x=0orx=-1
Thus, options (B) have two roots.
Options (C):
Factorize the equation x2+2x+2=0 by quadratic formula.
x2+2x+2=0x=-2±22-42221x=-2±4-162x=-2±-122x=-2±23i2
Options (C) have two roots as a result.
Hence, option (A) is correct.

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