Question

if alpha and beta are the zeroes of quadratic polynomial such that alpha plus beta equal to 24 and alpha minus beta equal to 8 find a qiadratic polynomial having alpha and beta as its zeroes

Answer 1

Alpha + beta =24 - [i]
Alpha - beta =8
So, (Alpha + beta) + (Alpha-beta)=24 + 8
Alpha + beta + Alpha - beta =32
Removing +beta and -beta we get,

Alpha + Alpha =32
Alpha=32÷2=16

Now by eq.[i]
16+beta =24
Beta =24-16=8

Required polynomial :-

K[x²-(alpha+beta)x + alpha ×beta]

K=1

x²-24x + (16×8)

Ans - x²-24x+128

My Request :- Don't copy the solution , first understand then try ro solve on ur own

Best regards
Vatsalya

Answer 2

the answer is x2 - 24x + 128