Question

solve the quadratic equation by using any method. write imaginary answers in simplified form using integers, fractions, or radicals.
$2t^2 + 3t = 0$
the solution set is {______}.

Explanation:

Step1: Factor the equation

Factor out \( t \) from the left - hand side of the equation \( 2t^{2}+3t = 0 \). We get \( t(2t + 3)=0 \).

Step2: Apply the zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both).

• Case 1: If \( t=0 \), the equation \( t(2t + 3)=0 \) is satisfied.
• Case 2: If \( 2t+3 = 0 \), we solve for \( t \). Subtract 3 from both sides: \( 2t=-3 \), then divide both sides by 2: \( t=-\frac{3}{2} \).

Answer:

\( 0,-\frac{3}{2} \)