Question

If 1/2 is root of X square + kx -5/4 = 0 then find valuable of k

Answer 1

$\huge{\mathfrak{\red{\underline{\underline{Answer:-}}}}}$

→ K = 2

$\large{\mathrm{\gray{Given :-}}}$

» x² + kx - 5/4 = 0

» 1/2 is a factor of polynomial x² + kx - 5/4 = 0

$\large{\mathrm{\gray{To \: Find:-}}}$Value of k

$\large{\mathrm{\gray{Solution :-}}}$

Put value of x

$\mathfrak{ { (\frac{1}{2}) }^{2} } + k( \frac{1}{2}) - \frac{5}{4}\\ \\\mathfrak{ { (\frac{1}{4}) } } + ( \frac{k}{2}) - \frac{5}{4} \\ \\ \mathfrak{ {\frac{1}{4} } - \frac{5}{4}} \: = ( \frac{ - k}{2}) \\ \\ \mathfrak{ \frac{1 - 5}{4} } =\frac{ - k}{2} \\ \\ \mathfrak{ \frac{ - 4}{4} } = \frac{ - k}{2} \\ \\ \mathfrak{{ \frac{{ - \cancel4}}{{ \cancel4}} }} = \frac{ - k}{2} \\ \\ \mathfrak{ - 1 \times 2} = - k \\ \\ \mathfrak{ - 2} = - k \\ \\ \mathfrak{{ \cancel - }2} = { \cancel - }k \\ \\\mathfrak{ 2} = k \\ \\ { \huge{ \pink{ \boxed{k = \mathfrak{2}}}}}$

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$\LARGE{\bf{\red{\boxed{T}}}}$${\bf{\pink{\boxed{h}}}}$${\bf{\orange{\boxed{e}}}}$$\LARGE{\bf{\blue{\boxed{S}}}}{\bf{\purple{\boxed{h}}}}{\bf{\pink{\boxed{e}}}}{\bf{\gray{\boxed{i}}}}{\bf{\green{\boxed{l}}}}{\bf{\boxed{d}}}$

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Answer 2

$\huge\sf\green{Solution\:is\: attached\:here:-}$