Question

If 1/2 is a root of the equation x^2+kx+5/2=0 then find the value of k

Answer 1

Hello friends!!

Here is your answer :

P(x) = x² + kx + 5/2 = 0

$\frac{1}{2} \: \: is \: root \: of \: p(x).$


Therefore,

$\\ p( \frac{1}{2} ) = 0$


$\\ p( \frac{ 1 }{2} ) = {( \frac{1}{2} )}^{2} + k( \frac{1}{2} ) + \frac{5}{2}$

$\\ = > 0 = \frac{1}{4} + \frac{k}{2} + \frac{5}{2}$


$\\ = > \frac{ - k}{2} = \frac{1 + 10}{4}$



$\\ = > - k = \frac{11}{4} \times 2$


$\\ = > - k = \frac{11}{2}$


$\\ = > k = \frac{ - 11}{2}$


$= > k \: = \: - 5.5$


Hope it helps you

^_^