Question

ANYONE ANSWER THIS ONE : I'll follow that person and mark the best answer brainliest​

Answer 1

Step-by-step explanation:

p(x)=ax^2+(a+b)x+b=0

=>ax^2+ax+bx+b=0

=>ax(x+1)+b(x+1)=0

=>(ax+b)(x+1)=0

Either,

ax+b=0

=>x= -b/a

or

x+1=0

=>x= -1

Therefore, the roots are -b/a and -1

Answer 2

Answer:

$\alpha = \frac{ - b}{a} \\ \\ \\ \beta = - 1$

Step-by-step explanation:

$p(x) = a {x}^{2} + (a + b)x + b \\ \\ Quadratic \: Formula = \frac{ - b \: + - \sqrt{ D} }{2a} \\ \\ \sqrt{D} = \sqrt{ {b}^{2} - 4ac} \\ \\ \\ Here \\a = a \\ b = a + b \\ c = b \\ \\ \\ \sqrt{ D} = \sqrt{ {b}^{2} - 4ac} \\ \\ \sqrt{D } = \sqrt{(a + b) ^{2} - 4 \times a \times b} \\ \\ \sqrt{D } = \sqrt{ {a }^{2} + {b}^{2} + 2ab - 4ab} \\ \\ \sqrt{D } = \sqrt{ {a}^{2} + {b}^{2} - 4ab} \\ \\ \sqrt{D } = \sqrt{(a - {b})^{2} } \\ \\ \sqrt{D } = \sqrt{(a - b)(a - b)} \\ \\ \sqrt{D } = a - b \\ \\ \\ \\ \alpha = \frac{ - b +\sqrt{D } }{2a} \\ \\ \alpha = \frac{ - (a + b) + a - b}{2a} \\ \\ \alpha = \frac{ - a - b +a - b }{2a} \\ \\ \alpha = \frac{ - 2b}{2a} \\ \\ \alpha = \frac{ - b}{a} \\ \\ \\ \\ \beta = \frac{ - b - \sqrt{D } }{2a} \\ \\ \beta = \frac{ - (a + b) - ( a - b)}{2a} \\ \\ \beta = \frac{ - a - b - a + b}{2a} \\ \\ \beta = \frac{ - 2a}{2a} \\ \\ \beta = - 1$

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