Question

plzzzzzzzzz answer this

Answer 1

Here I am writing Alpha as a and Beta as b.

Given x^2 - 8x + k.

On comparing with ax^2 + bx + c, we get

a = 1, b = -8, c = k


We know that Sum of roots = -(b)/a

                                              = -(-8)/1

                     a+b                   = 8.



We know that Product of roots = c/a

                        ab                         = k.




Now,

Given a^2 + b^2 = 40.

We know that (a + b)^2 = a^2 + b^2 + 2ab

                        (8)^2 = 40 + 2k

                        64 = 40 + 2k
 
                        64 - 40 = 2k

                         24 = 2k

                          24/2 = k

                          k = 12.


Therefore the value of k = 12.


Hope this helps!