Question

if alpha and beta are the zeros of the polynomial p (x) =5 x square - 3 x + 1 then find the value of (Alpha by beta + beta by Alpha)​

Answer 1

Question:

If @ and ß are the zeroes of the quadratic polynomial p(x) = 5x² - 3x + 1 then find the value of (@/ß + ß/@) .

Answer:

@/ß + ß/@ = –1/5

Note:

• The general for of a quadratic polynomial is given as : ax² + bx + c .

• Zeros of a polynomial are the possible values of unknown (variable) for which the polynomial becomes zero.

• If A and B are the zeros of quadratic polynomial ax² + bx + c then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

• If A and B are the zeros of any quadratic polynomial then that quadratic polynomial is given as : x² - (A+B)x + A•B

Solution:

The given quadratic polynomial is :

p(x) = 5x² - 3x + 1

Clearly, we have ;

a = 5

b = -3

c = 1

Also,

It is given that , @ and ß are the zeros of the given polynomial p(x) , thus ;

=> Sum of zeros = -b/a

=> @ + ß = -(-3)/5

=> @ + ß = 3/5 -------(1)

Also,

=> Product of zeros = c/a

=> @•ß = 1/5 --------(2)

Now,

@/ß + ß/@ = (@² + ß²)/@•ß

= [ (@ + ß)² - 2@•ß ]/@•ß

= (@ + ß)²/@•ß - 2

Using eq-(1) and eq-(2) , we have ;

@/ß + ß/@ = (3/5)²/(1/5) - 2

= (9/25)/(1/5) - 2

= 9•5/25 - 2

= 9/5 - 2

= (9 - 10)/5

= - 1/5

Hence,

The required value of (@/ß + ß/@) is –1/5 .