The roots of 4x^2 + 6px + 1 = 0 are equal,the | 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 $4x^2 + 6px + 1 = 0$,w

Vedclass · Accepted Answer

$\frac{2}{3}$

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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 $4x^2 + 6px + 1 = 0$,we have $a = 4$,$b = 6p$,and $c = 1$.Substituting these values into the discriminant formula:$(6p)^2 - 4(4)(1) = 0$$36p^2 - 16 = 0$$36p^2 = 16$$p^2 = \frac{16}{36} = \frac{4}{9}$Taking the square root on both sides,we get $p = \pm \frac{2}{3}$.Since $\frac{2}{3}$ is provided as an option,the correct value is $\frac{2}{3}$.

The roots of $4x^2 + 6px + 1 = 0$ are equal,then the value of $p$ is

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