Question

if alpha and beeta are the zeroes of a quadratic polynomial such that alpha+beeta =0 and alpha-beeta =8 find the quadratic polynomial having alpha and beeta as its zeroes​

Answer 1

Answer:

x²+8 = 0

Step-by-step explanation:

k[x² - (sum of zeros)×x + (product of zeros) ]

k[x²-0x + 8]

put k = 1

x²+8 = 0

Hope this will help you.

If so please mark me brainliest.

Answer 2

Let the polynomial be of form ax^2+bx+c=0.

Alpha+beta=0(given)

Alpha*beta=?

(alpha-beta)^2=alpha^2+beta^2-2alpha*beta

                           =(alpha+beta)^2-2alpha*beta-2alpha*beta

                           =(alpha+beta)^2-4alpha*beta

Given,alpha-beta=8 alpha+beta=0

So,8^2=0-4alpha*beta

Alpha*beta= -64/4 =-16

Quadratic polynomial formed is of the form x2-(alpha+beta)x+alpha*beta  

                                                                    =x2-0*x-16

So the quadratic polynomial is                        =x^2-16

hope you understand.