Question

If a and bare the zeroes of the polynomial x^2 + 4x + 3 find the polynomial where zeroes are 1+b/a and 1+a/b

Answer 1

HEY MATE HERE IS YOUR ANSWER

x^2 + 4x +3 =0

x^2 + x+ 3x +3 =0

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

(x+1 )(x+3)

x= -3 ,-1
a= -3 , b= -1

So for find polynomial whose zeros are 1+ b/a , 1+a/b

sum of zeroes = 1+ b/a + 1 + a/b
alpha + beta = 1 + -1/-3 + 1 + -3 /-1
= 2+ 1/3 + 3
= 5 +1/3
= 16/3
product of zeros = (1+ b/a)(1+ a/b)
alpha × beta = ( 1 + -1/-3)(1+-3/-1)
= (1+ 1/3)(1+3/1)
= (1+1/3)(4)
= 4 + 4/3
= 16 /3
For quadratic equation formula is
x^2 -(alpha + beta )x + alpha × beta
x^2 - (16/3)x + 16/3 =0
3x^2 -16x + 16 =0