Question

The nature of roots of quadratic equation 4x²+4√3x+3=0​

Answer 1

Answer:

The roots of the equation are Real and Equal.

Step-by-step explanation:

Please refer the attachment.

Regards.

Answer 2

Given:

A quadratic equation 4x²+4√3x+3=0​.

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 4x²+4√3x+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 real roots D > 0.

=> For equal roots D = 0.

=> For imaginary roots D < 0.

3. Substitute the values in the above formula,  

=> D = √[(4√3)² - 4(3)(4)]

=> D = √[48 - 48]

=> D = 0.

=> The value of D is 0. Hence the given equation has real and equal roots.

Therefore, the roots of the given quadratic equation are equal.