Which of the following equations have only one solution? Select all correct answers.x²-x-6=05 x2 + 20 x+ 20 = 09x2 - 25 = 04x2+4 x=012+

7 answers
Question:

Which of the following equations have only one solution? Select all correct answers. x²-x-6=0
5 x2 + 20 x+ 20 = 0
9x2 - 25 = 0
4x2+4 x=0
12+ 6 x+9= 0​

Answers

The equations which have only one solution is: 5x²+20x+20=0,

Step-by-step explanation:

5x^2 + 20x + 20 = 0

12+ 6x +9= 0​

Step-by-step explanation:

5x^2 + 20x + 20 = 0  /5             12 + 6x + 9 = 0        

x^2 + 4x + 4 = 0                          6x = -9-12

(x+2)^2=0                                    6x = -21

x + 2 = 0                                      x = -21/6

x=-2                                             x = -3.5

[tex]4x^2+4x=0 \\
4x(x+1)=0 \\
4x=0 \ \lor \ x+1=0 \\
x=0 \ \lor \ x=-1 \\
\hbox{two solutions} \\ \\
x^2+6x+9=0 \\
(x+3)^2=0 \\
x+3=0 \\
x=-3 \\
\hbox{one solution}[/tex]

[tex]9x^2-25=0 \\
(3x)^2-5^2=0 \\
(3x-5)(3x+5)=0 \\
3x-5=0 \ \lor \ 3x+5=0 \\
3x=5 \ \lor \ 3x=-5 \\
x=\frac{5}{3} \ \lor \ x=-\frac{5}{3} \\
\hbox{two solutions} \\ \\
5x^2+20x+20=0 \\
x^2+4x+4=0 \\
(x+2)^2=0 \\
x+2=0 \\
x=-2 \\
\hbox{one solution}[/tex]

[tex]x^2-x-6=0 \\
x^2+2x-3x-6=0 \\
x(x+2)-3(x+2)=0 \\
(x-3)(x+2)=0 \\
x-3=0 \ \lor \ x+2=0 \\
x=3 \ \lor \ x=-2 \\
\hbox{two solutions}[/tex]

The equations which have only one solution are: x²+6x+9=0 and 5x²+20x+20=0, 

[tex]4x^2+4x=0 \\
4x(x+1)=0 \\
4x=0 \ \lor \ x+1=0 \\
x=0 \ \lor \ x=-1 \\
\hbox{two solutions} \\ \\
x^2+6x+9=0 \\
(x+3)^2=0 \\
x+3=0 \\
x=-3 \\
\hbox{one solution}[/tex]

[tex]9x^2-25=0 \\
(3x)^2-5^2=0 \\
(3x-5)(3x+5)=0 \\
3x-5=0 \ \lor \ 3x+5=0 \\
3x=5 \ \lor \ 3x=-5 \\
x=\frac{5}{3} \ \lor \ x=-\frac{5}{3} \\
\hbox{two solutions} \\ \\
5x^2+20x+20=0 \\
x^2+4x+4=0 \\
(x+2)^2=0 \\
x+2=0 \\
x=-2 \\
\hbox{one solution}[/tex]

[tex]x^2-x-6=0 \\
x^2+2x-3x-6=0 \\
x(x+2)-3(x+2)=0 \\
(x-3)(x+2)=0 \\
x-3=0 \ \lor \ x+2=0 \\
x=3 \ \lor \ x=-2 \\
\hbox{two solutions}[/tex]

The equations which have only one solution are: x²+6x+9=0 and 5x²+20x+20=0, 

=0

Step-by-step explanation:

[tex]x \geqslant - 6[/tex]

step-by-step explanation:

it's is b

[tex]() solve the inequality below for x: -4x-11< 13[/tex]

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

pls mark as brainliest

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