The number of solutions of -3x2-x-5-x-3 is

Given equation nbsp;3x^2+x+5=(x 3)^2 ⇒ 3x^2+x+5=x^2 6x+9 ⇒ 2x^2+7x 4=0 ⇒ (x+4)(2x 1)=0 ⇒ x= 4, 12 Both these solutions does not satisfy x−3 gt;0 as square r ...

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Standard XIII

Mathematics

Roots under Different Values of Coefficients

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 B $0$
Given equation $3 x^{2} + x + 5 = (x - 3)^{2} \Rightarrow 3 x^{2} + x + 5 = x^{2} - 6 x + 9$
$\Rightarrow 2 x^{2} + 7 x - 4 = 0$
$\Rightarrow (x + 4) (2 x - 1) = 0$
$\Rightarrow x = - 4, \frac{1}{2}$
Both these solutions does not satisfy $x - 3 > 0$ as square root of a number is always positive.
Hence, there is no solution

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

The correct option is B 0Given equation 3x2+x+5=(x−3)2⇒3x2+x+5=x2−6x+9 ⇒2x2+7x−4=0 ⇒(x+4)(2x−1)=0 ⇒x=−4, 12 Both these solutions does not satisfy x−3>0 as square root of a number is always positive. Hence, there is no solution

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