Question

The root of the equation
(2x-1)+(x-1)=x+2 is​

Answer 1

Answer:

Quadratic equation : 2x

2

−2(2a+1)x+a(a+1)=0

Both roots are real, discriminant =D>0

Comparing with the standard quadratic equation Ax

2

+Bx+C=0, we get A=2>0.

Since, x=a lies between the two roots and A is positive, we have f(a)<0

⇒ 2(a)

2

−2(2a+1)(a)+a(a+1)<0

⇒ −a

2

−a<0

⇒ a

2

+a>0

⇒ a∈(−∞,−1)∪(0,∞)

Hence, options (A), (C) and (D) are correct.

Answer 2

(2x-1)+(x-1)=x+2

2x-1+x-1=x+2

3x-x = 2+1+1

2x = 4

x = 2

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