Question

Find the value of k of 2x²＋3x＋k are the following expressions positive

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:k=\frac{9}{8}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies 2x^{2} +3x + k= 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies 2x^{2} +3x + k= 0} \\ \\ \tt{\circ \: a = 2} \\ \\ \tt{\circ \: b = 3}\\\\ \tt{\circ \:c = k}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (3)^{2} - 4\times2\times k= 0 } \\ \\ \tt{ : \implies \: 9 -8k= 0 } \\\\ \tt{: \implies 9= 8k} \\ \\ \tt{: \implies k= \frac{9}{8}} \\ \\ \green{\tt{ \therefore k =\frac{9}{8} }}$

Answer 2

$\huge\bold\green{Question}$

Find the value of k of 2x²＋3x＋k are the following expressions positive

$\huge\bold\green{Answer}$

According to the question we have given :-

°•° Equation → 2x²＋3x＋k

Now , as said in question we have to find out the required value of “ k ”

So , let's start

$\begin{lgathered}\sf{ = 2x^{2} +3x + k= 0} \\ \\ \tt{ \: a = 2} \\ \\ \sf{ \: b = 3}\\\\ \sf{ \:c = k}\\ \\ \sf\green{Discriminant \: = 0} \\ \\ \sf{ \: D = {b}^{2} - 4ac = 0 } \\ \\ \sf{ {b}^{2} - 4ac = 0} \\ \\ \tt\green{Now \: substituting\: the \: given \: values\:in\: formula} \\ \sf{= (3)^{2} - 4\times2\times k= 0 } \\ \\ \sf{ = \: 9 -8k= 0 } \\\\ \sf{= 9= 8k} \\ \\ \sf{= k= \frac{9}{8}}\end{lgathered}$

Hence the required value of k is 9/8