Question

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

Answer 1

Answer:

k = 2

Explanation:

2/3 is a one root of given

quadratic equation 6x²-x-k=0,

we get

put x = 2/3 in the equation,

6(2/3)²-(2/3)-k=0

=> 6×(4/9)-(2/3)-k=0

=> 8/3-2/3-k=0

=> 6/3 - k = 0

=> 2-k=0

=> -k = -2

=> k = 2

Therefore,

k = 2

••••

Answer 2

According to the Question

Root = $\bf\huge\frac{2}{3}$

Quadratic equation 6 x²- x - k = 0

Substitute value of x

$\bf\huge 6\times (\frac{2}{3})^2 - \frac{2}{3} - k = 0$

$\bf\huge 6\times \frac{4}{9} - \frac{2}{3} - k = 0$

$\bf\huge\frac{8}{3} - \frac{2}{3} - k = 0$

$\bf\huge\frac{6}{3} - k = 0$

⇒ 2 - k = 0

⇒ -k = -2

⇒ k = 2