JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q63

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MathematicsSingle correct+4 / -1Question 63 of 90

The equation $\sqrt{3x^2+x+5}=x-3$ , where $x$ is real, has :

no solution

exactly one solution

exactly two solutions

exactly four solutions.

Answer and worked solution

Official answer: A

The right side must be non-negative, so $x\ge3$ . Squaring: $3x^2+x+5=x^2-6x+9$ , i.e. $2x^2+7x-4=0$ , so $x=\frac12$ or $-4$ . Neither satisfies $x\ge3$ : no solution.

Topics:Equations reducible to quadratic

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JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 63