Question

The solutions to :2x^2 - 10x + 13 = 0 are a+bi and a-bi, where a and b are positive. What is a*b?

Answer 1

Answer:

5

Step-by-step explanation:

Discriminant of this equation =

= ( - 10 )² - 4( 2 * 13 )

= 100 - 4( 26 )

= 100 - 104

= - 4

Using quadratic formula :

x = [ 10 ± √( - 4 ) ] / 2

= [ 10 ± 2i ] / 2

= 2( 5 ± i ) / 2

= 5 ± i

As given, x = a + bi and a - bi

= > 5 + i = a + bi or 5 - i = a - bi

Comparing values :

a = 5 ; b = 1

Hence ab = 5 * 1 = 5