Question

. Solve the equation 25x2 –30x+11=0. Show that roots are complex & conjugate

Answer 1

Answer:

Step-by-step explanation:

50-30x+11=0

-30x+11=0+50

-30x=50-11

x=39\3o

Answer 2

The roots of the equation are "complex and conjugate", shown.

Step-by-step explanation:

The given equation:

25$x^2$ – 30x + 11 = 0

Here, a = 25, b = - 30 and c = 11

Show that, the roots of the equations are complex and conjugate.

∴ D = $b^{2}-4ac$

= $(-30)^{2} -4(25)(11)$

= 900 - 1100

= - 200 < 0, the roots are complex.

x = $\dfrac{-b±\sqrt{D} }{2a}$

= $\dfrac{-(-30)±\sqrt{-200} }{2(25)}$

= $\dfrac{30±\sqrt{(1-)200} }{50}$

= $\dfrac{30±\sqrt{200i^2} }{50}$   [∵ $i^{2}$ = - 1]

= $\dfrac{30±10\sqrt{2}i }{50}$  

= $\dfrac{10(3±\sqrt{2}i )}{50}$  

= $\dfrac{(3±\sqrt{2}i )}{5}$  

= $\dfrac{3+\sqrt{2}i}{5}$  or, $\dfrac{3-\sqrt{2}i}{5}$, the roots are complex.

Thus, the roots of the equation are "complex and conjugate".