Final answer:
The quadratic equation in standard form is 4.90t² + 14.3t - 20.0 = 0 and it can be solved using the quadratic formula. Quadratic equations, or second-order polynomials, are essential in diverse scientific fields.
Step-by-step explanation:
The equation for a quadratic polynomial in standard form is ax² + bx + c = 0. When the coefficients (a, b, c) are given, we can write the specific equation. In the case you presented, the constants are a = 4.90, b = 14.3, and c = -20.0. Therefore, the quadratic equation in standard form is 4.90t² + 14.3t - 20.0 = 0. To solve this equation for 't', we can apply the quadratic formula, which is t = ∛(-b ± √(b² - 4ac)) / (2a).
In your example, this formula will provide the solution for t by substituting a, b, and c into the formula. If we consider an alternative quadratic equation presented as t² + 10t - 2000 = 0, it is already in standard form, and we can use the quadratic formula as described to find the solutions for t.
Quadratic equations are also known as second-order polynomials or quadratic functions. They are frequently encountered in various branches of mathematics and are pivotal in solving many problems in physics, engineering, and economics.