Quadratic Equations Quiz: Bank PO Practice (x and y Comparison)

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. I. x² − 7x + 12 = 0 II. y² − 11y + 30 = 0. Which relation between x and y is correct?

   • x > y
   • x < y
   • x >= y
   • Relationship cannot be established

   Answer: x < y. x = 3 or 4; y = 5 or 6. Every x is smaller than every y, so x < y.

2. I. x² + 9x + 20 = 0 II. y² + 7y + 12 = 0. Which relation between x and y is correct?

   • x > y
   • x < y
   • x <= y
   • Relationship cannot be established

   Answer: x <= y. x = −4 or −5; y = −3 or −4. x is never larger, and x = y = −4 is possible, so x <= y.

3. I. x² − x − 12 = 0 II. y² − 5y + 6 = 0. Which relation between x and y is correct?

   • x > y
   • x < y
   • x >= y
   • Relationship cannot be established

   Answer: Relationship cannot be established. x = 4 or −3; y = 2 or 3. x = 4 is above both y values but x = −3 is below them, so no single relation holds.

4. I. 2x² − 13x + 21 = 0 II. 3y² − 8y + 4 = 0. Which relation between x and y is correct?

   • x > y
   • x < y
   • x <= y
   • Relationship cannot be established

   Answer: x > y. x = 3 or 3.5 (split −13x as −6x − 7x); y = 2 or 2/3 (split −8y as −6y − 2y). Every x exceeds every y.

5. If p and q are the roots of 3x² − 12x + 7 = 0, what is the value of p² + q²?

   • 34/3
   • 38/3
   • 16
   • 28/3

   Answer: 34/3. p + q = 12/3 = 4 and pq = 7/3. p² + q² = (p + q)² − 2pq = 16 − 14/3 = 34/3.

6. For what positive value of k does x² − kx + 16 = 0 have equal roots?

   • 4
   • 16
   • 8
   • 6

   Answer: 8. Equal roots need discriminant 0: k² − 64 = 0, so k = 8 (taking the positive value).

7. Which quadratic equation has roots 5 and −3?

   • x² + 2x − 15 = 0
   • x² − 2x − 15 = 0
   • x² − 8x + 15 = 0
   • x² + 8x − 15 = 0

   Answer: x² − 2x − 15 = 0. x² − (sum)x + product = 0: sum = 2, product = −15, giving x² − 2x − 15 = 0.

8. One root of x² − 10x + k = 0 is 4. What is the value of k?

   • 20
   • 28
   • 16
   • 24

   Answer: 24. Sum of roots = 10, so the other root is 6, and k = product = 4 × 6 = 24. (Or substitute: 16 − 40 + k = 0.)

9. I. x² − 14x + 49 = 0 II. y² − 13y + 42 = 0. Which relation between x and y is correct?

   • x > y
   • x >= y
   • x < y
   • x <= y

   Answer: x >= y. x = 7 (a repeated root); y = 6 or 7. x is greater than or equal to every y, so x >= y.

10. I. x² − 5x + 6 = 0 II. y² + 5y + 6 = 0. Which relation between x and y is correct?

    • x < y
    • x <= y
    • x = y
    • x > y

    Answer: x > y. x = 2 or 3; y = −2 or −3. Changing the sign of the middle term flips the signs of the roots, so x > y.