Question

if α and β are the zeroes of x²+5x+6 find the value of α-¹β-¹​

Answer 1

Step-by-step explanation:

I/alpha ×1/bita

=1/alpha bita

=1/product of roots

The formula for product of roots =c/a

So 1/c/a

A/c

=1/6

So the answer =1/6

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Answer 2

Step-by-step explanation:

Given -

α and β are zeroes of the polynomial

p(x) = x² + 5x + 6

To Find -

Value of α-¹β-¹

» 1/α × 1/β

• » 1/αβ

x² + 5x + 6

here,

a = 1

b = 5

c = 6

Method 1 :-

As we know that :-

• αβ = c/a

» 6/1

• » 6

Then,

The value of 1/αβ is 1/6

Method 2 :-

Using Quadratic formula :-

• x = -b ± √b² - 4ac/2a

» -(5) ± √(5)² - 4×1×6/2(1)

» -5 ± √25 - 24/2

» -5 ± √1/2

» -5 ± 1/2

Zeroes are -

x = -5 - 1/2

» -6/2

• » -3

And

x = -5 + 1/2

» -4/2

• » -2

Then,

The value of 1/α × 1/β is

1/-3 × 1/-2

» 1/6

Hence,

The value of α-¹β-¹ is 6-¹.