Question

find the value of K so that the equation x2-4x+k=0 has equal roots.

Answer 1

Answer:

4

Step-by-step explanation:

p(x) = x² - 4x + k = 0

a = 1,   b = -4,   c = k

Given that p(x) has equal roots. So p(x) should be a perfect square.

Is there any feature for such quadratic polynomials in accordance with finding the value of k, which means any easy method? Let's see.

As p(x) has equal roots, so the discriminant is zero.

⇒ b² - 4ac = 0

⇒ b² = 4ac

⇒ b²/4a = c

Thus we got one feature, and this is most helpful for finding the value of k, because c = k. Thus,

⇒ k = b²/4a

⇒ k = (-4)² / (4 × 1)

⇒ k = 16 / 4

⇒ k = 4

Thus the value of k is 4.