Question

the difference between the roots of quadratic equation x^2-11x+k=0 is 3. Find the value of k​

Answer 1

Let l, m be the roots of the given equation that is of x^2 + kx + 3 =0 . Then from theory of quadratic equation, we must have ;

(l + m) = - k and (l· m) = 3 . Also it is given that

(l -m) = 2 . Now this implies that ;

4 = (l - m)^2 =(l + m)^2 - 4(l · m) = k^2 - (4×3) or

4 =k^2 -12 ===> k^2 = 16 which in turn gives

k = 4 and k = - 4 . when k = 4 , the equation becomes x^2 + 4x + 3 = (x + 3)(x + 1) = 0 , giving the two roots as -3 & -1 so the absolute difference between them is 2 . Similarly when k = - 4 , equation becomes as (x- 3)(x - 1) = 0 , so the roots are 3 & 1 , giving the difference between the roots equals 2.