Question

4.The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is



(a) ±√6

(b) ± 4

(c) ±3√2

(d) ±2√6​

Answer 1

Answer:

(d) ±2√6

Step-by-step explanation:

We know that an equation has 2 equal roots only when its discriminate, D = 0

⇒ b² - 4ac = 0

⇒ k² - 24 = 0

⇒ k² = 24

⇒ k = ±√24 = ±2√6

Hope this helps.....

Answer 2

Given:

A quadratic equation 2x² + kx + 3 = 0 has equal roots.

To Find:

The value of k such that the equation has equal roots is?

Solution:

The given problem can be solved using the concepts of quadratic equations.    

1. The given quadratic equation is 2x² + kx + 3 = 0  

2. For an equation to have equal roots the value of the discriminant is 0,  

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,  

=> Discriminant ( D ) = $\sqrt{b^2-4ac}$.  

=> For equal roots D = 0.  

3. Substitute the values in the above formula,  

=>  D = 0,  

=> √[(k)² - 4(2)(3)] = 0,

=> k² - 24 = 0,

=> k² = 24,

=> k = ±2√6.

Therefore, the values of k are ±2√6. Option D is the correct answer.