Solving Quadratic Equations With Exponents

TL;DR

Learn how to solve a quadratic equation involving exponents by factoring and using the zero product property.

Transcript

consider this problem two x squared minus seven x plus three all raised to the fourth power is equal to two thousand four hundred and one what is the value of x so feel free to take a minute and try to solve this problem so what do you think is the first thing that we need to do here our first step is we need to get rid of the exponent four so what... Read More

Key Insights

• 🙃 The exponents in an equation can be eliminated by raising both sides to an appropriate root.
• 😑 Factoring can be used to solve a quadratic equation with a trinomial expression.
• 0️⃣ The zero product property allows the solutions of a quadratic equation to be found by setting each factor equal to zero.

Questions & Answers

Q: What is the first step in solving the given problem?

The first step is to eliminate the exponent by raising both sides of the equation to the fourth root or by raising them to the power of one-fourth.

Q: How can the value of the fourth root of 2401 be found?

The fourth root of 2401 can be found by typing "2401 raised to the one over four" on a scientific calculator, resulting in the value seven.

Q: What method can be used to solve the resulting quadratic equation?

The quadratic equation can be solved by factoring it into two binomials using the factoring by grouping technique.

Q: How can the solutions to the quadratic equation be determined?

The solutions can be determined by setting each factor equal to zero and solving for x using the zero product property.

Summary & Key Takeaways

• The video teaches how to solve a quadratic equation with an exponent of four by raising both sides to the fourth root.

• After eliminating the exponent, the equation becomes a quadratic equation with a trinomial.

• The video demonstrates how to factor the quadratic equation using the factoring by grouping technique and how to solve for the values of x.