Question

If one root of the quadratic equation 6x2-x-k=0 is 2/3 then find the value of k

Answer 1

Answer:

6x²-x-k=0

where x=2/3

so,

6(2/3)²-2/3-k=0

6(4/9)-2/3=k

8/3-2/3=k

6/3=k

2=k

Answer 2

$\huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

★ Given :

Quadratic Equation:- 6x² - x - k = 0

One root of quadratic Equation is 2/3

★ To Find :

We have to find the valie of k.

★ Solution :

One root of quadratic Equation is 2/3.

So,

x = 2/3

$\rule{150}{2}$

(Putting Value of x as 2/3)

$\sf{6( \frac{2}{3})^{2} - \frac{2}{3} - k = 0} \\ \\ \sf{6( \frac{4}{9}) - \frac{2}{3} - k = 0 } \\ \\ \sf{ \frac{24}{9} - \frac{2}{3} - k = 0 } \\ \\ \bf{taking\: lcm} \\ \\ \sf{ \frac{24 - 6 - 9k}{9} = 0} \\ \\ \sf{18 - 9k = 0} \\ \\ \sf{ \cancel- 18 = \cancel - 9k} \\ \\ \sf{k = \frac{ \cancel{18}}{ \cancel{9}} } \\ \\ {\large{\boxed {\green{ \sf{k = 2}}}}}$