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Sagot :
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]
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
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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