Question

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Answer 1

Note: Here I am writing alpha as A and Beta as B.

Given Equation is x^2 + kx +12.

It is in the form of ax^2 + bx + c, We get

a = 1, b = k, c = 12.

Now,

We know that sum of roots(A + B) = -c/a

                                                          = -k/1

                                                           = -k.


We know that product of roots(AB) = c/a

                                                           = 12/1

                                                           = 12.



Given A - B = 1

We know that:

(A - B)^2 = (A + B)^2 - 4AB

   1           = (-k)^2 - 4(12)

    1          = k^2 - 48

   1  +  49  = k^2

   k = +7 (or) -7.


Hope this helps!