Roots of 2 k x^{2}+5 k x+2=0 are equal if k i | vedclass

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

Vedclass · Accepted Answer

$\frac{16}{25}$

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(B) For the quadratic equation $ax^{2}+bx+c=0$,the roots are equal if the discriminant $D = b^{2}-4ac = 0$.Given equation: $2 k x^{2}+5 k x+2=0$.Here,$a=2k$,$b=5k$,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 possible values for $k$: $k=0$ or $25k-16=0$.If $k=0$,the equation becomes $2=0$,which is not a quadratic equation. Therefore,$k 
eq 0$.Thus,$25k = 16$,which implies $k = \frac{16}{25}$.

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

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