- 1. John is 5 years older than twice his brother's age. If John is 29 years old, how old is his brother?
A) 8
B) 7
C) 10
D) 12
- 2. The product of two consecutive positive integers is 56. What is the smaller number?
A) 6
B) 8
C) 5
D) 7
- 3. What are the binomial factors of 𝑥2 − 22𝑥 + 121?
A) (x - 11)(x + 10)
B) (x - 10)(x + 12)
C) (x - 11)(x - 11)
D) (x + 1)(x + 1)
- 4. What are the solutions of the quadratic equation 𝑥2 − 81 = 0?
A) no solution
B) 8 and - 8
C) 9 and - 9
D) 7 and - 7
- 5. What is the standard form of the quadratic equation 3𝑥(4 + 𝑥) = 15?
A) 3x2 + 12x +15 = 0
B) 12x - 3x2 = 15
C) 12x2 - 3x - 15
D) 3x2 + 12x - 15 = 0
- 6. How do we write the quadratic equation whose roots are 4 and – 3?
A) x2 + x - 12 = 0
B) x2 - x - 12 = 0
C) x2 + 7x - 12
D) x2 - 7x - 21 = 0
- 7. What is the quadratic term of this equation 4𝑥2 + 3𝑥 − 2 = 0?
A) 3x
B) x2
C) 4x2
D) - 2
- 8. What is the constant term in this quadratic equation 4𝑥2 + 3𝑥 − 2 = 0?
A) 2
B) 4x2
C) -2
D) 3x
- 9. What must be added to both sides in order to complete the square in the equation 𝑥2 + 10𝑥 + ( ) = 9 + ( ) ?
A) 100
B) 10
C) 5
D) 25
- 10. How many real roots does the quadratic equation 4𝑥2 = 324 have?
A) 1
B) 0
C) 2
D) 3
- 11. What is the value of coefficient 𝑏 in this equation 6𝑥2 − 8𝑥 + 10 = 0 ?
A) -8x
B) - 8
C) 8
D) 6
- 12. What are the roots of (𝑥 − 4)2 = 49?
A) 11 and - 3
B) 7 and 4
C) - 11 and 3
D) 7 and - 4
- 13. Which of the following is the product of the roots of 𝑥2 + 3𝑥 − 27 = 0?
A) 27
B) 24
C) 3
D) - 27
- 14. What is the nature of roots of the quadratic equation if the value of its discriminant is greater than zero and a perfect square?
A) The roots are rational and not equal
B) The roots are not real
C) The roots are real, rational, and equal
D) The roots are irrational and not equal
- 15. What is the nature of the roots of the quadratic equation if the value of its discriminant is negative?
A) the roots are rational and not equal
B) the roots are irrational and not equal
C) the roots are real, rational, and equal
D) the roots are not real
- 16. Which is true for the equation 𝑥2 − 5𝑥 + 12 = 0?
A) the roots are rational and not equal
B) the roots are rational and equal
C) the roots are not real
D) the roots are irrational and not equal
- 17. In a quadratic equation, what do you call the value 𝑏2 − 4𝑎𝑐?
A) the discriminant
B) the divisor
C) the diameter
D) the denominator
- 18. Which of the following quadratic equations has no real roots?
A) x2 + 8x + 15
B) x2 - 2x - 15
C) x2 - 2x + 15 = 0
D) x2 - 8x + 15 = 0
- 19. What is the sum of the roots of 𝑥2 = 10𝑥 − 25?
A) 25
B) 10
C) -25
D) -10
- 20. What is the sum of the roots of a quadratic equation 𝑥2 + 6𝑥 − 14 = 0?
A) - 6
B) 14
C) 6
D) -14
- 21. What is the product of the roots of a quadratic equation 𝑥 2 + 6𝑥 − 14 = 0?
A) -14
B) 14
C) -6
D) 6
- 22. What is the formula for the product of roots of a quadratic equation ?
A) b2 - 4ac
B) c/ a
C) b/ 2
D) -b/a
- 23. Transform the quadratic equation (x+3)(x - 4) = 5 to its standard form.
A) x2 - 7x + 12
B) x2 - x - 17
C) x2 -7x - 12 = 5
D) x2 + x + 17
- 24. What are the solutions of the quadratic equation 6𝑥2 − 294 = 0 ?
A) 7 and - 7
B) 8 and - 8
C) 11 and - 11
D) 9 and - 9
- 25. What is the simplified and standard form of quadratic equation
(𝒙− 𝟔)^𝟐 + (𝒙+ 𝟕)^𝟐 = 𝟗𝟕?
A) 2x2 - 14 x - 97 = 0
B) 2x2 + 2x = 12
C) x2 + x - 6 = 0
D) 2x2 +x - 97 = 0
- 26. Solve the roots of the Quadratic Equation (𝒙 − 𝟓)^𝟐 = 𝟗 .
A) -2 and - 8
B) - 2 and 8
C) 2 and 8
D) 2 and - 8
- 27. Solve the roots of the Quadratic Equation (𝒙 − 𝟔)^𝟐 + (𝒙 + 𝟕)^𝟐 = 𝟗𝟕
A) 2 and -3
B) - 2 and 3
C) 2 and 3
D) -2 and -3
- 28. What is the sum of the roots of a quadratic equation 𝑥2 + 6𝑥 − 14 = 0?
A) -6
B) -14
C) 6
D) 14
- 29. What is the value of the discriminant for the equation 3x2 + 2x + 1 = 0?
A) 8
B) - 8
C) - 10
D) 6
- 30. The quadratic equation x2 + 1=0 has real solutions.
A) false
B) true
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