NCERT Class X Chapter 4: Quadratic Equation Exercise 4.3 Question 2 (i)

NCERT Class X Chapter 4: Quadratic Equation Exercise 4.3 2 (i)

Question:

Find the values of k for each of the following quadratic equations, so that they have two equal roots: 2x2 + kx + 3 = 0.

Given:

The quadratic equation: 2x2 + kx + 3 = 0

To Find:

The value(s) of 'k' such that the equation has two equal roots.

Formula:

For quadratic equation of the form ax2 + bx + c = 0 to have two equal roots, its discriminant (Δ) must be equal to zero.

Δ = b2 - 4ac = 0

Solution:

The given quadratic equation is 2x2 + kx + 3 = 0.
Comparing it with the standard form ax2 + bx + c = 0, we have:

a = 2

b = k

c = 3
For two equal roots, the discriminant must be zero (Δ = 0):

⇒ b2 - 4ac = 0

⇒ (k)2 - 4(2)(3) = 0

⇒ k2 - 24 = 0

⇒ k2 = 24

⇒ k = ±√24

⇒ k = ±√(4 × 6)

⇒ k = ±2√6

Result:


The values of k for which the quadratic equation 2x2 + kx + 3 = 0 has two equal roots are k = 2√6 and k = -2√6.
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