Question

if the roots of x square - MX + n is equal to zero are consecutive odd integers then find the value of the discriminant of the equation​

Answer 1

Answer:

4

Step-by-step explanation:

X^2 - MX + n = 0 ......(1)

Let the two consecutive odd integers be 2k-1, 2k+1

Since the sum of roots of (1) is M (formula -b/a in ax^2 + bx + c = 0),

2k-1 + 2k + 1 = 4k = M  ....... (2)

Product of roots of (1) is n (formula c/a).

Hence (2k-1)*(2k+1) = n (or) n = 4k^2 - 1 .......(3)

Discriminant of (1) is given by the formula D = b^2 - 4ac

substituting values for a,b,c from (1) above:

(or) D = (-M)^2 - 4*1*n = M^2 - 4n

Substituting from (2) and (3) above,

D = (4k)^2 - 4*(4k^2 - 1) = 16k^2 - 16k^2 + 4 = 4