1.

Find roots of the equation by quadratic formula : x^(2)+x-(a+2)(a+1)=0

Answer»

Solution :The given equation is
`x^(2)+x-(a+2)(a+1)=0`
Comparing it with `AX^(2)+Bx+C=0`, we get `A=1,B=1andC=-(a+2)(a+1)`
`:.x-B+-sqrt(B^(2)-4AC)/(2A)`
`x=(-1+-sqrt(1^(2)-4xx1xx[-(a+2)(a+1)]))/(2XX1)`
`impliesx=(-1+-sqrt(1+4(a^(2)+33a+2)))/(2)`
`impliesx=(-1+-sqrt(1+4a^(2)+12a+8))/(2)`
`impliesx=(-1+-sqrt(4a^(2)+12a+9))/(2)`
`impliesx=(-1+-sqrt((2a+3)^(2)))/(2)`
`impliesx=(-1+-(2a+3)^(2))/(2)`
`impliesx=(-1+2a+3^(2))/(2)and (-1-2a-3)/(2)`
`impliesx=(2a+2)/(2)and (-2a-4)/(2)`
`impliesx=(a+1)and-(a+2)` are ROOTS of the equation.


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