Find the value of k for which the quadratic equation, kx(x - 3) + 9=0 has two real equal roots

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:

Math worksheets and
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Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.

Given quadratic equation is:
kx( x − 2 )+ 6 = 0
⇒ kx2 − 2kx + 6 = 0For a quadratic equation to have equal roots,

b2 − 4ac = 0

Concept: Application of Quadratic Equation

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

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