The roots of 2 k x^{2} + 5 k x + 2 = 0 are eq | vedclass

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(C) For a quadratic equation $ax^{2} + bx + c = 0$,the roots are equal if the discriminant $D = b^{2} - 4ac = 0$.Given the equation $2 k x^{2} + 5 k x

Vedclass · Accepted Answer

$\frac{16}{25}$

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(C) For a quadratic equation $ax^{2} + bx + c = 0$,the roots are equal if the discriminant $D = b^{2} - 4ac = 0$.Given the equation $2 k x^{2} + 5 k x + 2 = 0$,we have $a = 2k$,$b = 5k$,and $c = 2$.Substituting these values into the discriminant formula:$(5k)^{2} - 4(2k)(2) = 0$$25k^{2} - 16k = 0$Factor out $k$:$k(25k - 16) = 0$This gives two possibilities: $k = 0$ or $25k - 16 = 0$.If $k = 0$,the equation becomes $2 = 0$,which is impossible. Thus,$k 
eq 0$.Therefore,$25k - 16 = 0$,which implies $k = \frac{16}{25}$.

The roots of $2 k x^{2} + 5 k x + 2 = 0$ are equal if $k$ is equal to

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