Question

If a and B are the zeroes of x2 + 5x + 6 find the value of alpha ^-1 + beta^-1.

Answer 1

Answer:

Given that -

α and β are the zeroes of the quadratic polynomial x² + 5x + 6.

We know that,

The standard form of the quadratic polynomial is ax² + bx + c. Here,

a = 1

b = 5

c = 6

Sum of zeroes =  

⇒ α + β =  

⇒ α + β = - 5

Product of zeroes =  

⇒ αβ =  

⇒ αβ = 6

To find :

= α - 1 + β - 1

= α + β - 2

= - 5 - 2

= - 7

Hence, the answer is -7.

Answer 2

Answer:

Here,

The given quadratic polynomial is :

x² + 5x + 6 .

Clearly,

a = 1

b = 5

c = 6

Also,

It is given that , α and ß are the zeros of the given quadratic polynomial .

Thus,

Sum of zeros = -b/a

α + ß = -5/1 = -5

Also,

Product of zeros = c/a

αß = 6/1 = 6

Now,

α^(-1) + ß^(-1) = 1/α + 1/ß

= (ß + α) / αß

= (α + ß) / αß

= -5/6

Hence,

The required answer is (-5/6) .