Quadratic Equation problems
- 1. ?. 10x 2 ? 7x + 1 = 0
?. 35y 2 -12y + 1 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 4
Explanation:
- 2. ?. 6x 2 + 77x + 121 = 0
?. y 2 + 9y ? 22 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer:
Explanation:
- 3. ?. x 2 ? 6x = 7
?. 2y 2 + 13y + 15 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 2
Explanation:
- 4. In the following determine the set of value of P for which the given quadratic equation has real roots. Px2 + 4 x + 1 = 0
Options- A. P ? 4
- B. P > 4
- C. P ? 4
- D. P ? 4 Discuss
Correct Answer: P ? 4
Explanation:
Given :- Px2 + 4x + 1 = 0
Compare with Ax 2 + Bx + C = 0, we get
A = P, B = 4, C = 1
For real roots,
B2 - 4AC ? 0
? 16 - 4P ? 0
? 16 ? 4P
? P ? 16/4 ? P ? 4.
Hence , required answer is option C .
- 5. The roots of the equation ?7x2 - 6x - 13?7 = 0 are
Options- A. - ?7, - 13 ?7 7
- B. ?7, - 13 ?7 7
- C. - ?7, 13 ?7 7
- D. None of these Discuss
Correct Answer: - ?7, 13 ?7 7
Explanation:
- 6. In the following, find the value (s) of P so that the given equation has equal roots 3x 2 - 5x + P = 0
Options- A. - 25 12
- B. 25 6
- C. 25 12
- D. - 25 6 Discuss
Correct Answer: 25 12
Explanation:
- 7. With respect to the roots of x2 - x - 2 = 0, we can say that :
Options- A. both of them are natural numbers
- B. both of them are integers
- C. the latter of the two is negative
- D. None of these Discuss
Correct Answer: both of them are integers
Explanation:
Given :- x2 - x - 2 = 0
The given equation is of the form
ax2 + bx + c = 0
Here , a = 1 , b = -1 , c = - 2
Now, D2 = b2 - 4ac = ( -1 )2 - 4 x 1 x ( - 2 )
D = ?9 = 3
So, roots are rational .
Hence, both the roots must be integers.
- 8. If ?, ? are the roots of the quadratic equation x2 - 8x + k = 0, find the value of k such the ?2 + ?2 = 40
Options- A. 12
- B. 14
- C. 10
- D. 16 Discuss
Correct Answer: 12
Explanation:
- 9. ?. x 2 ? 11x + 24 = 0
?. 2y 2 ? 9y + 9 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 2
Explanation:
- 10.
?. 2 × 4 - 3 × 4 = x10/7 x 4/7 x 4/7
?. y 3 + 783 = 999
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 4
Explanation:
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