Question

Solve the equation by factoring. $$4 t^{2}+9 t+2=0$$

   Solve the equation by factoring.
$$4 t^{2}+9 t+2=0$$

Contemporary Precalculus

Contemporary Precalculus

Thomas W.… 5th Edition

Chapter 1, Problem 19

Instant Answer

Solved by Expert Charles Carter

07/18/2020

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This gives us $4t^2 + 9t + 8 = 0$. Show more…

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Solve the equation by factoring. $$4 t^{2}+9 t+2=0$$

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Key Concepts

Zero Product Property

The zero product property states that if a product of factors equals zero, then at least one of the factors must be zero. This property is critical after factoring a quadratic because it allows each factor to be set individually equal to zero, leading to the determination of the solutions to the equation.

Factoring Quadratics

Factoring is a technique used to express a quadratic equation as a product of two binomial expressions. This involves finding two numbers that multiply to ac and add to b, allowing the quadratic to be broken down into simpler factors that can be set equal to zero.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation typically expressed in the form ax^2 + bx + c = 0. It involves finding the values of the variable that satisfy this equality, which often represent the points where a quadratic function intersects the x-axis.

Standard Form

Writing a quadratic equation in the standard form, ax^2 + bx + c = 0, is essential for applying solution methods like factoring, completing the square, or the quadratic formula. This form clearly identifies the coefficients needed for factoring and other techniques.

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