Q5 of 242 Page 8

Find the least positive value of k for which the equation has real roots.

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D ≥ 0, roots are real

⇒ D = k² – 16

Thus, k² – 16 ≥ 0

⇒ k ≥ 4 or k ≤-4

Thus, least positive value of k is 4.

In the following, determine the set of values of k for which the given quadratic equation has real roots:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

For what value of k, , is a perfect square.

Find the values of k for which the given quadratic equation has real and distinct roots:

(i)

(ii)

(iii)

If the roots of the equation are equal, then prove that 2b = a + c.