The roots of the equation -3 x-1-1-x areA- roots doesnot existB- 0C- 1D- 0-1

The correct option is A roots doesnot exist given equation is √(3x+1) + 1 = √(x) ⇒ √(3x+1) = √(x) 1 Squaring both the sides, we get 3x + 1 = x + 1 2√(x) ⇒ ...

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Standard XII

Mathematics

Roots of a Quadratic Equation

The roots of ...

Question

The roots of the equation $\sqrt{3 x + 1} + 1$ = $\sqrt{x}$ are

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0,1

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roots doesnot exist

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Solution

The correct option is D
roots doesnot exist

given equation is $\sqrt{3 x + 1} + 1$ = $\sqrt{x}$

⇒ $\sqrt{3 x + 1}$ = $\sqrt{x}$ - 1

Squaring both the sides, we get 3 $x$ + 1 = $x$ + 1 -2 $\sqrt{x}$

⇒ 2 $\sqrt{x}$ + 2 $x$ = 0 (irrational function)

Thus $x$ ≠ 0 and $x$ ≠ 1, Since equation is non-quadratic equation.

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The roots of the equation √3x+1+1 = √x are

The correct option is D roots doesnot exist given equation is √3x+1+1 = √x ⇒ √3x+1 = √x - 1 Squaring both the sides, we get 3x + 1 = x + 1 -2√x ⇒ 2√x + 2x = 0 (irrational function) Thus x ≠ 0 and x ≠ 1, Since equation is non-quadratic equation.

The roots of the equation $\sqrt{3 x + 1} + 1$ = $\sqrt{x}$ are