Question

If a and B are the zeroes of x² + 5x+6 find the value of a¹ +²¹.

Answer 1

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

$\sf{\underline{\overline{\pink{Given\:}}}}$

α and в are zeroes of the polynomial

p(x) = x² + 5x + 6

$\sf{\underline{\overline{\green{To\: find}}}}$

Value of a-¹3-¹

» 1/α × 1/в

» 1/αв

x² + 5x + 6

here,

a = 1

b = 5

C = 6

Method 1 :-

$\sf{\underline{\overline{\red{As \: we\:know\:that\:}}}}$

ab = c/a

» 6/1

» 6

Then,

The value of 1/ab 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 x 1/в is

1/-3 x 1/-2

» 1/6

Hence,

The value of α-¹в-¹ is 6-¹.

Answer 2

ANSWER

Given

• α and в are zeroes of the polynomial

• p(x) = x² + 5x + 6

Tofind

• Value of a-¹3-¹

» 1/α × 1/в

» 1/αв

x² + 5x + 6

here,

a = 1

b = 5

C = 6

Method 1 :-

As we know that

ab = c/a

» 6/1

» 6

Then,

The value of 1/ab 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 x 1/в is

1/-3 x 1/-2

» 1/6

Hence,

The value of α-¹в-¹ is 6-¹.