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Sagot :

Answer:

x= -3.936 and -0.064

Step-by-step explanation:

I simplified the equation to 40u^2 +16u + 1. Then I just graphed it and found that the zeroes were -3.936 and -0.064.

DᴀʀᴋPᴀʀᴀᴅᴏx

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Here we go ~

Let's calculate its discriminant :

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 = 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 - 40 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 1 = 0[/tex]

Here, if we equate it with general equation,

  • a = 4

  • b = 16

  • c = 1

[tex]\qquad \sf  \dashrightarrow \: disciminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (4 \times 4 \times 1) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (16) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(16 - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 240[/tex]

Now, since discriminant is positive ; it has two real roots ~

The roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - b \pm \sqrt{ d } }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm \sqrt{ 240 } }{2 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm 4\sqrt{ 15 } }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ 4(- 4\pm \sqrt{ 15 }) }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4\pm \sqrt{ 15 } }{2} [/tex]

So, the required roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4 - \sqrt{ 15 } }{2} \: \: and \: \: \dfrac{ - 4 + \sqrt{15} }{2} [/tex]

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