Understanding Quadratic Equations

The video tutorial explains how to find numbers whose sum with their square equals 90. It begins by defining a variable and setting up a quadratic equation. The equation is solved by factoring, yielding two solutions: 9 and -10. Both solutions are verified by substituting them back into the original equation. The tutorial concludes by confirming that both solutions satisfy the given condition.

What is the initial problem statement discussed in the video?

• The quotient of a number and its square is 90.

• The sum of a number and its square is 90.

• The difference between a number and its square is 90.

• The product of a number and its square is 90.

What variable is used to represent the number in the problem?

• y

• n

• z

• x

How is the quadratic equation rearranged for solving?

• x^2 - x = 90

• x^2 + x = 90

• x^2 - x - 90 = 0

• x^2 + x - 90 = 0

What is the purpose of factoring the quadratic equation?

• To simplify the equation

• To convert it into a linear equation

• To find the roots of the equation

• To eliminate the variable

Which pair of factors is used to factor the equation?

• x - 9 and x + 10

• x + 9 and x - 10

• x - 10 and x + 9

• x + 10 and x - 9

What are the solutions obtained after solving the linear equations?

• x = 10 and x = -9

• x = 9 and x = -10

• x = -9 and x = 10

• x = -10 and x = 9

How is the solution x = 9 verified?

• By checking if 9 / 9^2 equals 90

• By checking if 9 * 9^2 equals 90

• By checking if 9 - 9^2 equals 90

• By checking if 9 + 9^2 equals 90

What is the result of substituting x = -10 into the equation?

• -10 * 100 equals 90

• -10 - 100 equals 90

• -10 / 100 equals 90

• -10 + 100 equals 90

Why is it important to use parentheses when substituting negative values?

• To correctly apply the exponent

• To ensure correct multiplication

• To avoid syntax errors

• To simplify the equation

What conclusion is drawn after verifying both solutions?

• Neither solution satisfies the condition

• The solutions are incorrect

• Both solutions satisfy the condition

• Only one solution satisfies the condition