Solving a Quadratic Equation Raised to a Power

The video tutorial guides viewers through solving an algebraic equation involving an exponent. It begins by simplifying the equation by removing the exponent, then transforms it into a quadratic equation. The quadratic is factored using grouping, and the zero product property is applied to find the solutions for x. Finally, the solutions are verified by substituting them back into the original equation to ensure correctness.

What is the first step in solving the equation (2x^2 - 7x + 3)^4 = 2401?

• Add 7 to both sides

• Take the fourth root of both sides

• Multiply both sides by 4

• Subtract 3 from both sides

What is the fourth root of 2401?

• 7

• 9

• 6

• 8

After simplifying the equation, what form does it take?

• Cubic equation

• Exponential equation

• Linear equation

• Quadratic equation

Which method is used to factor the quadratic equation 2x^2 - 7x - 4 = 0?

• Completing the square

• Factoring by grouping

• Using the quadratic formula

• Synthetic division

What is the greatest common factor (GCF) taken out from the first two terms during factoring?

• 7

• 4

• 2x

• x

What property is used to solve the equation after factoring?

• Zero product property

• Distributive property

• Associative property

• Commutative property

What are the solutions obtained after solving the factored equation?

• x = 6 and x = 0

• x = 4 and x = -1/2

• x = 3 and x = -1

• x = 5 and x = 1/2

How do you verify if the solutions are correct?

• By graphing the equation

• By substituting the solutions back into the original equation

• By checking the discriminant

• By using a calculator

What is the result when x = 4 is substituted back into the original equation?

• 2400

• 2401

• 2402

• 2403

What is the result when x = -1/2 is substituted back into the original equation?

• 2403

• 2402

• 2401

• 2400