Question

Find the value of k for which the equation 3x^2-6x+k=0 has distinct and real roots.

Answer 1

Hey...


The answer is in the attachment.

Hope this would help you.

__________________________________________

#Saadya

Answer 2

Given as :

The quadratic equation

3 x² - 6 x + k = 0

The roots of this equation is distinct and real roots

To Find :

The vale of k

Solution :

The standard quadratic equation  a x² + b x + c = 0

For real roots of quadratic equation

Discriminant = D $>$ 0

i.e $b^{2}$  - 4 a c $>$ 0

Now, compare standard equation with given quadratic equation i,e                  3 x² - 6 x + k $>$ 0

   So,  $(-6)^{2}$  - 4 × 3 × k $>$ 0

Or,   36 - 12 k $>$ 0

Or,          12 k $>$ 36

∴                 k $>$ $\dfrac{36}{12}$

i.e               k $>$ 3

So, The value of k $>$ 3

Hence The value of k for which roots of equation are real and distinct is $>$ 3 Answer