Question

If alpha and beta are zeros of the given polynomial p(x)= 6x^2+x-2,then find there value if alpha/beta+ beta/alpha

Answer 1

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Answer 2

Answer:

The value of ( α / β ) + ( β / α ) is - 25 / 12.

Step-by-step-explanation:

The given quadratic polynomial is 6x² + x - 2.

We have given that,

α and β are the zeros of quadratic polynomial.

Comparing the quadratic polynomial with ax² + bx + c, we get,

• a = 6
• b = 1
• c = - 2

We know that,

Sum of zeros = - b / a

⇒ α + β = - 1 / 6

And,

Product of zeros = c / a

⇒ αβ = - 2 / 6

⇒ αβ = - 1 / 3

Now,

( α / β ) + ( β / α ) = ( α² + β² ) / ( αβ )

We know that,

( α + β )² = α² + 2αβ + β²

∴ α² + β² = ( α + β )² - 2αβ

⇒ ( α / β ) + ( β / α ) = [ ( - 1 / 6 )² - 2 * ( - 1 / 3 ) ] / ( - 1 / 3 )

⇒ ( α / β ) + ( β / α ) = [ ( 1 / 36 ) + ( 2 / 3 ) ] / ( - 1 / 3 )

⇒ ( α / β ) + ( β / α ) = [ ( 3 + 72 ) / ( 36 * 3 ) ] / ( - 1 / 3 )

⇒ ( α / β ) + ( β / α ) = [ 75 / ( 36 * 3 ) ] / ( - 1 / 3 )

⇒( α / β ) + ( β / α ) = - 75 / ( 36 * 3 ) * 3

⇒ ( α / β ) + ( β / α ) = - 75 / 36

⇒ ( α / β ) + ( β / α ) = - 25 / 12

∴ The value of ( α / β ) + ( β / α ) is - 25 / 12.