For what value of k can the quadratic polynom | vedclass

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(B) quadratic polynomial $az^{2} + bz + c$ can be factored into real linear factors if and only if its discriminant $D = b^{2} - 4ac$ is greater than

Vedclass · Accepted Answer

$k \leq \frac{25}{12}$

Vedclass · Answer

(B) quadratic polynomial $az^{2} + bz + c$ can be factored into real linear factors if and only if its discriminant $D = b^{2} - 4ac$ is greater than or equal to $0$.Given the polynomial $3z^{2} + 5z + k$,we have $a = 3$,$b = 5$,and $c = k$.The discriminant is $D = (5)^{2} - 4(3)(k) = 25 - 12k$.For the polynomial to have real linear factors,we require $D \geq 0$.Therefore,$25 - 12k \geq 0$.$25 \geq 12k$.$k \leq \frac{25}{12}$.

For what value of $k$ can the quadratic polynomial $3z^{2} + 5z + k$ be factored into a product of real linear factors?

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