Question

For what positive values of k, does the quadratic equation 3x^2-kx+3=0 not have real roots

Answer 1

hey here is ur answer :-

equation have no real roots so

b²-4ac > 0


k² - 36> 0


k > 6

Answer 2

Given:

A quadratic equation 3x² -kx + 3 = 0 has no real roots.

To Find:

The value of k such that the equation does not have real roots is?

Solution:

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

1. The given quadratic equation is 3x² - 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(3)(3)] < 0,

=> k² -36 = 0,

=> k < √(36),

=> k < ±6,

=> The positive values of the equation k < ±6 is k belongs to (0,6). ( 0 and 6 are not included)

Therefore, the positive values of k are k belongs to (0,6).