Question

If alpha, beta are the zeros of the polynomial p(x)= x2 + 1, then find value of
Alpha +beta/(alpha x beta)^2

Answer 1

Answer:

alpha+beta = -b/a

where b is the coefficient of X here X is not present so coefficient is 0,

then alpha+ beta =0

then alpha+beta/(alpha×beta)^2 is also 0

Answer 2

Step-by-step explanation:

Given :-

α and β are the zeros of the polynomial

P(x)= x²+ 1.

To find :-

Find value of ( α+β )/(αβ)² ?

Solution :-

Given Quadratic Polynomial is P(x) = x²+1

On comparing with the standard quadratic polynomial ax²+bx+c

a = 1

b = 0

Since there is no term with the coefficient of x

c = 1

Given zeroes are α and β

We know that

Sum of the zeores = α+β = -b/a

=> α+β = -0/1

=> α+β = 0 --------------(1)

Product of the zeroes = αβ= c/a

=> αβ = 1/1

=> αβ = 1 ----------------(2)

Now the value of ( α+β )/(αβ)²

=> 0/1²

=> 0/1

=> 0

Therefore, ( α+β )/(αβ)² = 0

Answer:-

The value of ( α+β )/(αβ)² for the given problem is 0

Used formulae:-

• The standard quadratic polynomial is ax²+bx+c

• Sum of the zeores = α+β = -b/a

• Product of the zeroes = αβ= c/a