For which value of k,are the roots of the equ | vedclass

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(B) The given quadratic equation is $2x^2 + 5x + k = 0$. For the roots of a quadratic equation with rational coefficients to be rational,the discrimin

Vedclass · Accepted Answer

$\frac{25}{8}$

Vedclass · Answer

(B) The given quadratic equation is $2x^2 + 5x + k = 0$. For the roots of a quadratic equation with rational coefficients to be rational,the discriminant $D = b^2 - 4ac$ must be a perfect square of a rational number. Here,$a = 2$,$b = 5$,and $c = k$. $D = (5)^2 - 4(2)(k) = 25 - 8k$. For $D$ to be a perfect square,we test the given options: If $k = \frac{25}{8}$,then $D = 25 - 8(\frac{25}{8}) = 25 - 25 = 0$. Since $0$ is a perfect square $(0^2 = 0)$,the roots are rational. Therefore,$k = \frac{25}{8}$ is the correct value. Thus,option $B$ is correct.

For which value of $k$,are the roots of the equation $2x^2 + 5x + k = 0$ rational?

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