Question

0.3 If a and B are the roots of the equation 2x +3v3x -6=0 then the value of 2 + B2 is
(a) ) 3/4
(b) 51/4
(c) 33/4
(d) 39/4​

Answer 1

Answer:

Given: (a): p(x) = 8x² – 19x – 15, (b) q(x) = 4√3 x² + 5x – 2√3,

f(x) = 5x -4√3 + 2√3 x²

To find: The roots of given equations and verify them.

Solution:

So as we need to find the roots, lets write the first equation:

p(x) = 8x² – 19x – 15

formula to find roots are = -b ±√D/2a

= 19 ± √((-19)² - 4(8)(-15))/ 2(8)

= 19 ± √361 + 480 / 16

= 19 ± √841 / 16

= 19 ± 29 / 16

48/16, -10/16

x = 3, -5/8

Now solving the next equation, we get:

q(x) = 4√3 x² + 5x – 2√3

applying the same formula of roots:

= -5 ± √((5)² - 4(4√3)( – 2√3))/ 2(4√3)

= -5 ± √(25 + 96)/ 8√3

= -5 ± √(121)/ 8√3

= -5 ± 11/ 8√3

= -16/8√3, 6/8√3

x = -2/√3 , √3/4

Now solving the next equation, we get:

f(x) = 2√3 x² + 5x - 4√3

applying the same formula of roots:

= -5 ± √25 - 4( 2√3)(- 4√3 )/2(2√3)

= -5 ± √25 + 96 / 4√3

= -5 ± 11 / 4√3

= -16/4√3, 6/ 4√3

x = -4/√3 , √3/2

Answer:

So the roots of the equations are:

p(x) = 8x² – 19x – 15, x = 3, -5/8

q(x) = 4√3 x² + 5x – 2√3, x = -2/√3 , √3/4

f(x) = 5x -4√3 + 2√3 x² , x = -4/√3 , √3/2