Final answer:
To determine the value of p for the equation to have coincident roots, we need to set the discriminant equal to zero and solve for p. In this case, p = -1/2.
Step-by-step explanation:
To have coincident roots, the discriminant of the quadratic equation must be equal to zero. The discriminant is given by B²-4AC, where A, B, and C are the coefficients of the quadratic equation. In this case, the quadratic equation is t² + p² - 2(p+1)t = 0. Comparing this to the standard form Ax² + Bx + C = 0, we can see that A = 1, B = -2(p+1), and C = p². Substituting these values, we get (-2(p+1))² - 4(1)(p²) = 0. Simplifying the equation gives 4p² + 8p + 4 - 4p² = 0.
Combine like terms to get 8p + 4 = 0. Solving for p gives p = -4/8 = -1/2.