Question

If α and ß are the zeroes of the polynomial x²-5x+6. Then the values of α⁴ ß²+ α²ß ⁴ is​

Answer 1

Step-by-step explanation:

It is given that à and ß are the zeroes of polynomial x²- 5x+6

Let Polynomial be f(x) = x²- 5x+6

{ On comparing; a = 1 , b = -5 and c = 6 }

Here, Relationship Between Zeros:

☞ Sum of Zeroes = -b/a

= -(-5)/1

= 5

☞ Product of Zeros = c/a

= 6/1

= 6

Now, We have to Find the Value of 1/à + 1/b - 2àß

☛ 1/à + 1/b - 2àß

= à+ß/àß - 2àß

= 5/6 - 2*6

= 5/6 - 12

= 5-72

= - 67

Therefore, Value of 1/à + 1/b - 2àß is -67.

Answer 2

Solution:

It is given that à and ß are the zeroes of polynomial x²- 5x+6

Let Polynomial be f(x) = x²- 5x+6

{ On comparing; a = 1 , b = -5 and c = 6 }

Here, Relationship Between Zeros:

☞ Sum of Zeroes = -b/a

= -(-5)/1

= 5

☞ Product of Zeros = c/a

= 6/1

= 6

Now, We have to Find the Value of 1/à + 1/b - 2àß

☛ 1/à + 1/b - 2àß

= à+ß/àß - 2àß

= 5/6 - 2*6

= 5/6 - 12

= 5-72

= - 67

Therefore, Value of 1/à + 1/b - 2àß is -67.