Question

If x = 2/3 is a solution of the quadratic equation 7x^2 + mx – 3 = 0; find the value of m.

Answer 1

Given:

(i) x = 2/3 is a solution of the quadratic equation 7x² + mx - 3 = 0

To find:

(i) The value of m.

Solution:

Given, the quadratic equation is:

7x² + mx - 3 = 0

As, x = 2/3 satisfies the equation, we put x = 2/3 in the equation and equate it to 0.

So, 7(2/3)² + m(2/3) - 3 =0

⇒  7 (4/9) + 2m/3 - 3 = 0

⇒ 28/9 - 3 + 2m/3 = 0

⇒ 2m/3 + 1/9 = 0

⇒ 2m/3 = - 1/9

⇒ 6m = 1

⇒ m = 1/6

The value of m is 1/6.

Answer 2

GIVEN :

$x =\frac{2}{3}$ is a solution of the quadratic equation $7x^2 + mx - 3 = 0$

TO FIND :

The value of m in the given quadratic equation.

SOLUTION:

Given quadratic equation is $7x^2 + mx - 3 = 0$

From the given we have that $x =\frac{2}{3}$ is a solution of the given quadratic equation.

∴ $x =\frac{2}{3}$ satisfies the given quadratic equation.

Put $x =\frac{2}{3}$ in the given quadratic equation  $7x^2 + mx - 3 = 0$ we get

$7(\frac{2}{3})^2 + m(\frac{2}{3}) - 3 = 0$

$7(\frac{4}{9})+ \frac{2m}{3} - 3 = 0$

$\frac{28}{9}+ \frac{2m}{3} - 3 = 0$

$\frac{28+6m-9}{9}=0$

$28+6m-9=0$

19+6m=0

6m=-19

$m=-\frac{19}{6}$

∴ the value of m is $-\frac{19}{6}$