Question

If alpha and beta are the zero of the polynomial 2x^2-5x+7find the value of 1/alpha+1/beta

Answer 1

α and β are the zeroes of the polynomial 2x² - 5x + 7 .

a = 2

b = -5

c = 7

★ Sum of the zeroes :

α + β = -b/a

⇒ α + β = -(-5 ) / 2

⇒ α + β = 5/2

★ Product of the zeroes :

αβ = c/a

⇒ αβ = 7/2

Now,

1/α + 1/β [ Given ]

⇒ β + α / αβ

⇒ ( α + β ) / αβ

Substituting the values, we get

⇒ 5/2 / 7/2

⇒ 5/2 × 2/7

⇒ 5/7

Hence the value of 1/α + 1/β is 5/7 .

Additional information:-

Relationship between zeroes:-

1. Linear :

k = - constant term/Coefficient of x

2. Cubic :

★Sum of zeroes = - Coefficient of x²/Coefficient of x³

★ Product of zeroes = - Constant term/Coefficient of x³

★ Sum of the Product of zeroes taken 2 at a time = Coefficient of x/Coefficient of x³

Answer 2

SOLUTION :

=>Let α and β are the zeroes of the polynomial 2x²-5x+7.

=> On comparing with ax²+bx + c = 0 , we get

•a = 2

•b = -5

•c = 7

•Sum of zeroes ,

=> α + β = -b/a

=> α + β = -(-5)/2

=> α + β = 5 / 2

.°. Sum of zeroes = 5/2 .

• Product of zeroes,

=> αβ = c/a

=> αβ = 7/2

.°. Product of zeroes = 7/2 .

Now,

=> 1/α + 1/β ---------[ Given ]

=> (α + β) / αβ

=> 5/2 / 7/2

=> 5/2 × 2/7

=> 5/7 .

.°. (1/α + 1/β) = 5/7 .