Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x² + kx + 3 = 0   (ii) kx (x - 2) + 6 = 0

Solution:

If a quadratic equation ax² + bx + c = 0 has two equal real roots, we know that, discriminant  b² - 4ac = 0

(i) 2x² + kx + 3 = 0

a = 2, b = k, c = 3

b² - 4ac = 0

(k)² - 4(2)(3) = 0

k² - 24 = 0

k² = 24

k = √24

k = ± √2 × 2 × 2 × 3

k = ± 2√6

(ii) kx (x - 2) + 6 = 0

kx² - 2kx + 6 = 0

a = k, b = - 2k, c = 6

b² - 4ac = 0

(-2k)² - 4(k)(6) = 0

4k² - 24k = 0

4k (k - 6) = 0

k = 6 and k = 0

If we consider the value of k as 0, then the equation will no longer be quadratic.

Therefore, k = 6

☛ Check: NCERT Solutions Class 10 Maths Chapter 4

---

Video Solution:

Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) 2x² + kx + 3 = 0 (ii) kx (x - 2) + 6 = 0

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.4 Question 2

Summary:

The values of k for each of the following quadratic equations (i) 2x² + kx + 3 = 0 (ii) kx (x - 2) + 6 = 0 have two equal roots are (i) ± 2√6 and (ii) k = 6 respectively.

---

☛ Related Questions:

• Find the nature of the roots of the following quadratic equations, if the real root exist, find them: i) 2x² - 3x + 5 = 0 ii) 3x2 - 4√3x + 4 = 0 iii) 2x² - 6x + 3 = 0
• Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.
• Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
• Is it possible to design a rectangular park of perimeter 80 m and area 400 m^2? If so, find its length and breadth.