Quadratic Equations Practice Problems: Level 01

Q1. The difference between the roots of a quadratic equation 6x2 + wx + 1 = 0 is 1/6. If w > 0, then the value of w is
A. 6
B. – 5
C. 5
D. 10
Q2. If the roots x1 and x2 of the quadratic equation satisfy the condition 7x2 – 4x1 = 47. The quadratic expression is x2 – 2x + c = 0, find the value of c.
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A. – 15
B. 15
C. – 6
D. None of these
Q.3. If (x2 y2) = 16 and xy = -15. Which of the following is a possible value of (x + y), if (x + y) is a positive number.
A. 3
B. 2
C. 5
D. None of these
Q.4. From any two numbers x and y, we define x * y = x + 0.5 y – xy. Suppose that both x and y are greater than 0.5, then x * x < y ×y if :
A. 1 > x > y
B. x > 1 > y
C. y > 1 > x
D. 1 > y > x
Q.5. The sum of the squares of two consecutive natural numbers is 85. Find those numbers.
A. 6, 7
B. 5, 8
C. 6, 8
D. -8, 6
Q.6. The sum of the squares of two consecutive odd natural numbers is 130. Find those numbers.
A. 3, 5
B. 7, 9
C. 5, 7
D. 7, -9
Q.7. The sum of a natural number and its reciprocal is 50/7. What is the number?
A. 7
B. 10
C. 1/5
D. 5
Q8. The difference between a natural number and twice its reciprocal is 47/7. What is that number?
A. 8
B. 9
C. 7
D. 1/7
Q9. The length of a rectangular field is less than twice its breadth by 5 metres. Its area is 700 square metres. Find the length and breadth of the field.
A. 35 m, 20 m
B. 25 m, 28 m
C. 70 m, 10 m
D. 35 m, 35 m
Q10. The base of a triangle is greater than twice its height by 1 cm. The area of the triangle is 18 sq. cm. Find the base and height of the triangle.
A. 18 cm, 2 cm
B. 9 cm, 4 cm
C. 6 cm, 9 cm
D. 6 cm, 7 cm
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