Question

If a and B are the zeroes of the quadratic polynomial 6x2 - 37x + 6, then find the value of 1/α+1/β​

Answer 1

Explanation:

α and β are zeroes of quadratic polynomial 6x² - 37x + 6

Polynomial = 6x² - 37x + 6

a = 6

b = -37

c = 6

→ Sum of zeroes = -b/a

→ α + β = -(-37)/6

→ α + β = 37/6 ....2)

→ Product of zeroes = c/a

→ αβ = 6/6

→ αβ = 1 ......1)

Now, Finding value of 1/α+1/β

→ 1/α+1/β = (β + α)/αβ

▶ Putting values of α + β and αβ from 1) and 2)

→ 1/α+1/β = 37/6/1

→ 1/α+1/β = 37/6

Hence,

Value of 1/α+1/β = 37/6.

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• α and β are zeroes of quadratic polynomial 6x² - 37x + 6.

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

• The value of 1/α+1/β

Formula to be used :-

• Sum of zeroes = -b/a

• Product of zeroes = c/a

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Given that,

Polynomial __ 6x² - 37x + 6

Where,

a = 6

b = -37

c = 6

________________________________________________

Now find sum and product of zeroes

★ Sum of zeroes = -b/a

α + β = -(-37)/6

α + β = 37/6

★ Product of zeroes = c/a

αβ = 6/6

αβ = 1

________________________________________________

Now, find the value of 1/α+1/β.

1/α+1/β

= (β + α)/αβ

(Putting acquired values)

= 37/6/1

= 37/6

Therefore , value of 1/α+1/β is = 37/6