Question

if one of the values of x of the equation 2x² - 6x +k =0 be 1/2 ( a+5i) find the values of a and K ?​

Answer 1

Answer:

2(a-5i)²/2-6(a+5i)/2+k=0 is the answer of this question

Answer 2

Given equation :  2x - 6x + k = 0

Given root in complex form :  $\frac{1}{2}(a+5i)$

other root = $\frac{1}{2}(a-5i)$

Sum of roots

= $\frac{1}{2}(a+5i)+\frac{1}{2}(a-5i)$

= $\frac{1}{2}(a+5i+a-5i)$

= $-(\frac{-6}{2})$

= 3

2a = 3

$\boxed{\bold{a=\frac{3}{2}}}$

Product of roots =  $\frac{k}{2}$

= $\frac{1}{2}(a+5i)\times \frac{1}{2}(a-5i)$

⇒ 2k = $a^2-25i^2$

⇒ 2k = $a^2+25$

Substituting the value of a in the equation,

⇒ 2k = $(\frac{3}{2})^2+25$

⇒ 2k = $\frac{9}{4}+25$

⇒ 2k = $\frac{100+9}{4}$

⇒ 2k = $\frac{109}{4}$

$\boxed{\bold{k = \frac{109}{8}}}$