Question

F(x) = 6x2 + x - 2, find alpha/beta + beta/alpha

Answer 1

Answer:

F(x) = 6x² + x - 2

On comparing the given equation by the standard form of quadratic equation, ax² + bx + c = 0

a = 6, b = 1, c = - 2

Here, we have ;

Sum of zeroes = - b/a

⇒ α + β = - 1/6

Product of zeroes = c/a

⇒ αβ = - 2/6

Here's the solution ;

$= \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } \\ \\ = \frac{ \alpha {}^{2} + \beta {}^{2} }{ \alpha \beta } \\ \\ = \frac{( \frac{ - 1}{6}) {}^{2} - 2 \times ( \frac{ - 2}{6})}{ \frac{ - 2}{6} } \\ \\ = \frac{ \frac{1}{36} + \frac{4}{6} }{ \frac{ - 2}{6} } \\ \\ = \frac{1 + 24}{36} \div ( \frac{ - 2}{6} ) \\ \\ = \frac{25}{36} \times ( \frac{ - 6}{2} ) \\ \\ = \boxed{ \bf \frac{ - 25}{12}}$

Hence, the answer is - 25/12.

___________________

Identity used ;

• ( a² + b² ) = ( a + b )² - 2ab

Answer 2

F(x) = 6x² + x - 2

6x² + x - 2=0

6x² - 3x +4x - 2=0

3x(2x-1) +2(2x-1) = 0

(3x+2) (2x-1)=0

3x+2=0 or 2x-1=0

3x= - 2 or 2x = 1

x = -2/3 or x = 1/2

Alpha = - 2/3 and beta = 1/2

=Alpha /beta + beta/alpha

= (-2/3)/(1/2) + (1/2)/(-2/3)

= - 2/3 ×2 + 1/2 ×3/-2

= - 4/3 + (-2/6)

= (-8 - 2)/6

= - 10/ 6

= - 5/3