Question

If α and β be the zeroes of the polynomial x^2 + 4x + 3, find the quadratic polynomial whose zeroes are 1+α/β and 1+β/α

Answer 1

Answer:

Step-by-step explanation:

p(x)= x^2 + 4x + 3

now factorise,

x^2 + 3x+ 1x + 3

x( x + 3 ) + 1( x+ 3)

(x+1) (x+3)

thus, x = -3 and x = -1

thus, α = -3    β = -1

find the quadratic polynomial whose zeroes are

1+α/β and 1+β/α

1+-3/-1 and 1+-1/-3  (substituting the values)

1+3/1 and -1+-1/3  

4  and  0/3

4 and 0

thus the Zeros of new equation are 2 and 0

Sum =

0 + 2 = 2

Product =

0 × 2 = 0

using the formula to form a quadratic polynomial

x^2 - (sum of zeroes)x + product of zeroes

sunstituting values

x^2 - 2x + 0

i.e

Ans, x^2 - 2x