Question

find the value of k for which the quadratic equation 4 x square - 2 + 1 X + K + 4 is equal to zero has equal roots

Answer 1

if it has equal roots then b^2-4ac=0.solve it and then you will get the value of k

Answer 2

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

$\green{\tt{\therefore{Value\:of\:k=-1.9375}}}$

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

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies 4x^{2} -2+x + k+4 = 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies 4x^{2} +x + k+2= 0} \\ \\ \tt{\circ \: a = 4} \\ \\ \tt{\circ \: b = 1}\\\\ \tt{\circ \:c = (k+2)}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (1)^{2} - 4\times4\times (k+2)= 0 } \\ \\ \tt{: \implies \: 1 -16k-32 = 0 } \\ \\ \tt{ : \implies \: -16k-31 = 0 } \\\\ \tt{: \implies 16k= -31} \\ \\ \tt{: \implies k= \frac{-31}{16}} \\ \\ \green{\tt{: \implies k = -1.9375 }}$