Question

• find the value of k for the quadrati
equation 2x² + kx +3= 0 such that it
has two equal roots.​

Answer 1

Required Answer:-

Given:

• 2x² + kx + 3 = 0

To find:

• The value of k such that the roots are equal.

Solution:

The discriminant of the quadratic equation tells the nature of roots of the given equation.

1. If the discriminant is equal to zero, then roots are equal.
2. If the discriminant is less than zero, roots are imaginary.
3. If the discriminant is greater than zero then roots are real and unequal.

Here, we will form an equation and after solving the equation, we will get the result.

Given equation is,

➡ 2x² + kx + 3 = 0

Here,

a (coefficient of x²) = 2

b (coefficient of x) = k

c = (coefficient of x^0) = 3

Now, discriminant is given by the formula,

➡ Δ = b² - 4ac

Here,

Δ = k² - 4 × 2 × 3 = k² - 24

If the roots are equal, then,

➡ Δ = 0

➡ k² - 24 = 0

➡ k² = 24

➡ k = ±√24

➡ k = ±2√6

Hence, the possible values of k such that the roots are equal is 2√6 and -2√6

Answer 2

answer in the image

hope it helps