Question

What is the value of K for which the quadratic equation 3x2-kx+k=0 has equal roots?

Answer 1

Answer:

the values of k for which the quadratic equation 3x^2−2kx+12=0 will have equal roots are 6 and

−6.

Step-by-step explanation:

The given quadratic equation is 3x^2 −2kx+12=0

On comparing it with the general quadratic equation ax^2+bx+c=0, we obtain

a=3,b=−2k and c=12

Discriminant, ′ D ′ of the given quadratic equation is given by

D=b^2 −4ac

=(−2k) 2 −4×3×12

=4k 2 −144

For equal roots of the given quadratic equations, Discriminant will be equal to 0.

i.e., D=0

⇒4k^2 −144=0

⇒4(k^2−36)=0

⇒k^2 =36

⇒k=±6

Therefore, the values of k for which the quadratic equation 3x 2−2kx+12=0 will have equal roots are 6 and −6.

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Answer 2

Given:

A quadratic equation 3x² -k x + k = 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   3x² - kx + k = 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)(k)] = 0,

=> k² -12k = 0,

=> k(k-12) = 0,

=> k = 0 (OR) k =12.

Therefore, the values of k are 0 and 12.