Question

if the alpha and beta are the zeros of a quadratic polynomial such that alpha + beta is equals to 24 and Alpha minus beta is equals to 8 then find the quadratic polynomial having alpha and beta as its zeros and also verify the relationship between the zeros and its coefficient

Answer 1

apply the formula alpha = 16. beta = 8

Answer 2

let alpha = w and beta = m for convenience
w-m = 8 given
w= 8+m
we know that m + w = -b/a
subsituting the values
according to ques , w+m = 24
m+8+m = 24
2m= 16
m= 8 , 8+ w = 24 ,
w = 16
24= -b/a
b = -24 , a = 1
now as we know the values of m and w and also know that m*w = c/a
8*16 = 128
c = 128 and a = 1
hence polynomial x^2 -24x+128