Jerry787354
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please help me please
[tex] {x}^{2} + 5x + 4 \\ \\ x {}^{2} -8x - 7 [/tex]
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Sagot :

Bora77

Answer:

[tex] {x}^{2} + 5x + 4 \\ \\ {x}^{2} + 4x + 1x + 4 \\ \\ x(x + 4) + 1(x + 4) \\ \\ (x + 4)(x + 1) \\ \\ {x}^{2} - 8x - 7 \\ \\ {x}^{2} - 7x + 1x + 7 \\ \\ x(x - 7) + 1( \times - ) \\ \\ (x - 7)(x + 7)[/tex]

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Question 1 ~

  • [tex] {x}^{2} + 5x + 4[/tex]

  • [tex] {x}^{2} + 4x + x + 4[/tex]

  • [tex]x( x + 4) + 1(x + 4)[/tex]

  • [tex](x + 4)(x + 1)[/tex]

So, the roots are ~

  • [tex] \boxed{x = - 4}[/tex]

and

  • [tex] \boxed{x = - 1}[/tex]

Question 2 ~

  • [tex] {x}^{2} - 8x - 7[/tex]

let's use the quadratic formula for this one ~

(because it can't be solved through middle term split method)

[tex] \boxed{ \mathrm{ \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}[/tex]

where,

  • b = -8 (Coefficient of x)

  • a = 1 (Coefficient of x²)

  • c = -7 (Constant)

now, let's plug the values to find the roots ~

  • [tex] \dfrac{ - ( - 8) \pm \sqrt{( - 8) {}^{2} - (4 \times 1 \times - 7) } }{2 \times 1} [/tex]

  • [tex] \dfrac{8 \pm \sqrt{64 - ( - 28)} }{2} [/tex]

  • [tex] \dfrac{8 \pm \sqrt{64 + 28} }{2} [/tex]

  • [tex] \dfrac{8 \pm \sqrt{92} }{2} [/tex]

  • [tex] \dfrac{8 \pm4 \sqrt{23} }{2} [/tex]

  • [tex] \dfrac{2(4 \pm2 \sqrt{23)} }{2} [/tex]

  • [tex]4 \pm2 \sqrt{23} [/tex]

So, the roots are ~

  • [tex] \boxed{x = 4 + 2 \sqrt{23} }[/tex]

and

  • [tex] \boxed{x = 4 - 2 \sqrt{23} }[/tex]

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