Final answer:
The degree of the polynomial for the quadratic equation in standard form at² + bt + c = 0 is 2. To solve for t using the quadratic formula, the equation must equal zero and the coefficients a, b, and c are inserted into the formula to find the two potential solutions for t.
Step-by-step explanation:
For the equation t−42=213, the given information appears to be misunderstood or incorrectly presented as this specific equation is linear, not quadratic, and does not reflect the standard form of a quadratic equation at² + bt + c = 0. However, for a quadratic equation of the form at² + bt + c = 0, the degree of the polynomial is 2 because the highest power of the variable t is 2.
To use the quadratic formula −b ± √b² - 4ac / 2a to solve a quadratic equation, the equation must first be arranged so that one side equals zero, such as t² + 10t - 200 = 0. The coefficients a, b, and c from this quadratic equation would then be used in the quadratic formula to find the values of t. This process yields two solutions, which can be calculated and checked for accuracy.