The number of solutions of -3 x2-x-5-x-3 isA- 0B- 1C- 2D- 4

The correct option is A 0 Note that we must have 3x^2+x+5 ≥ 0 and x 3 ≥ 0 or x≥ 3 √(3x^2+x+5)=x 3...(1) Squaring both sides of (1), we get 3x^2+x+5=x^2 6x+9 ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

The number of...

Question

The number of solutions of $\sqrt{3 x^{2} + x + 5} = x - 3$ is

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Solution

The correct option is A
0

Note that we must have $3 x^{2} + x + 5 \geq 0 a n d x - 3 \geq 0 o r x \geq 3$

$\sqrt{3 x^{2} + x + 5} = x - 3... (1)$

Squaring both sides of (1), we get

$3 x^{2} + x + 5 = x^{2} - 6 x + 9 \Rightarrow 2 x^{2} + 7 x - 4 = 0 \Rightarrow (2 x - 1) (x + 4) = 0 \Rightarrow x = \frac{1}{2}, - 4$

None of these satisfy the inequality $x \geq 3$ Thus, (1) has no solution.

Suggest Corrections

The number of solutions of √3x2+x+5=x−3 is

The correct option is A 0 Note that we must have 3x2+x+5≥0 and x−3≥0 or x≥3 √3x2+x+5=x−3...(1) Squaring both sides of (1), we get 3x2+x+5=x2−6x+9⇒2x2+7x−4=0⇒(2x−1)(x+4)=0⇒x=12,−4 None of these satisfy the inequality x≥3 Thus, (1) has no solution.

The number of solutions of $\sqrt{3 x^{2} + x + 5} = x - 3$ is