State True or False. The equation 2x $^{2}$ + 3x+1 = 0 has an irrational root

True

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False

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Solution

The correct option is B False
Given equation is $2 x^{2} + 3 x + 1 = 0$

It is of the form $a x^{2} + b x + c = 0$

$\Rightarrow 2 x^{2} + 3 x + 1 = 0$

$\Rightarrow 2 x^{2} + 2 x + x + 1 = 0$

$\Rightarrow 2 x (x + 1) + 1 (x + 1) = 0$

$\Rightarrow (2 x + 1) (x + 1) = 0$

$\Rightarrow x = - 1, - \frac{1}{2}$

So, x can take values $(- 1, - \frac{1}{2})$ . It can be expressed as the ratio of two integers suppose ( $- \frac{1}{1} = - 1$ and $- \frac{1}{2}$ is self-explanatory).

So, it does not have any irrational root both rational root. So, above statement is false.

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