Question

The zeroes of the quadratic polynomial x ^2 + kx + K where K is not equal to zeroes
(a)cannot both be positive
(b)cannot both be negative
(c)are always unequal
(d)are always equal
Please I want with explaination​

Answer 1

Answer:

Step-by-step explanation:

The zeroes of the quadratic polynomial x ^2 + kx + K k≠0 cannot both be positive.

Proof:

       Given equation is

       x ^2 + kx + K, k≠0

       Here,

               a = 1, b = c = k   ----------(1)

        Case (i): k < 0

               a > 0, b < 0, c < 0   [from (1)]

          ⇒ Both zeroes have opposite signs   -------------(2)

       Case (ii): k > 0

               a > 0, b > 0, c > 0    [from (1)]

          ⇒ Both zeroes are negative                --------------(3)

  ∴ From (1) and (2), we can conclude that both zeroes of given quadratic polynomial cannot be positive.

Hope it helps.