Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots

To find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots, we can use the discriminant of the quadratic equation. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

In this case, the quadratic equation is px(x – 3) + 9 = 0. We can expand this equation to get px^2 - 3px + 9 = 0. Comparing this with the standard form of a quadratic equation, we have a = p, b = -3p, and c = 9.

Now, we can calculate the discriminant. Substituting the values of a, b, and c into the formula, we get (-3p)^2 - 4(p)(9). Simplifying this expression, we have 9p^2 - 36p.

For the quadratic equation to have two equal roots, the discriminant must be equal to zero. So, we set 9p^2 - 36p = 0 and solve for p.

Factoring out p from the equation, we get p(9p - 36) = 0. Setting each factor equal to zero, we have p = 0 and 9p - 36 = 0.

Solving the second equation, we get 9p = 36, which gives p = 4.

Therefore, the value of p that makes the quadratic equation px(x – 3) + 9 = 0 have two equal roots is p = 4.