Quadratic Equation problems
- 1. The roots of the equation ax 2 + ( 4a 2 - 3b )x - 12ab = 0 are
Options- A. 4a , 3b a
- B. 4a , - 3b a
- C. - 4a , 3b a
- D. - 4a , - 3b a Discuss
Correct Answer: - 4a , 3b a
Explanation:
- 2. If ? and ? are the roots of the equation ax 2 + bx + c = 0, find the value of ?2 + ?2
Options- A. b 2 - 2ac 2a 2
- B. b 2 + 2ac a 2
- C. b 2 + 2ac a 2a
- D. b 2 - 2ac a 2 Discuss
Correct Answer: b 2 - 2ac a 2
Explanation:
- 3. An equation equivalent to the quadratic equation x2 ? 6x + 5 = 0 is :
Options- A. 6x2 - 5x +1 = 0
- B. x2 - 5x + 6 = 0
- C. 5x2 - 6x +1 = 0
- D. | x - 3 | = 2 Discuss
Correct Answer: | x - 3 | = 2
Explanation:
We can say that ,
The given quadratic equation x2 ? 6x + 5 = 0 ? ( x - 5 )( x - 1 ) = 0 ? x = 5 or 1
Now , | x - 3 | = 2 ? ( x - 3 ) = 2 or - ( x - 3 ) = 2 ? x = 3 + 2 = 5 or x = 3 - 2 = 1
? x2 - 6x + 5 = 0 and | x - 3 | = 2 are equivalent.
- 4. ?. 6x2 + 41x + 63 = 0
?. 4y2 + 8y + 3 = 0
Options- A. Relationship between x and y cannot be established
- B. x ? y
- C. x < y
- D. x > y Discuss
Correct Answer: x < y
Explanation:
- 5. ?. x 2 + 10x + 24 = 0
?. 4y 2 ? 17y + 18 = 0
Options- A. x ? y
- B. x ? y
- C. Relationship between x and y cannot be established
- D. x > y Discuss
Correct Answer:
Explanation:
- 6. ?. x 2 ? 20x + 91= 0
?. y 2 ? 32y + 247= 0
Options- A. x > y
- B. Relationship between x and y cannot be established
- C. x ? y
- D. x ? y Discuss
Correct Answer: x ? y
Explanation:
According to question ,
?. x2 ? 20x + 91= 0
? x2 ? 13x ? 7x + 91 = 0
? x(x ? 13) ? 7(x ? 13) = 0
? (x ? 7)(x ? 13) = 0
? x = 13, 7
?. y2 ? 32y + 247= 0
? y2 ? 19y ? 13y + 247 = 0
? y(y ? 19) ? 13(y ? 19) = 0
? (y ? 13)(y ? 19) = 0
? y = 13, 19
Hence, x ? y is required answer .
- 7. ?. 3x 2 ? 20x ?32 = 0
?. 2y 2 ? 3y ? 20 = 0
Options- A. x < y
- B. x ? y
- C. x > y
- D. Relationship between x and y cannot be established Discuss
Correct Answer: Relationship between x and y cannot be established
Explanation:
- 8. ?. 24x 2 + 38x + 15 = 0
?.12y 2 + 28y + 15 = 0
Options- A. x ? y
- B. x > y
- C. x ? y
- D. x < y Discuss
Correct Answer: x ? y
Explanation:
- 9. The value of k for which the roots ?, ? of the equation : x2 ? 6x + k = 0 satisfy the relation 3? + 2? = 20, is
Options- A. 8
- B. - 8
- C. 16
- D. - 16 Discuss
Correct Answer: 8
Explanation:
According to question , we have
The roots ?, ? of the equation : x2 ? 6x + k = 0
On comparing with ax2 + bx + c = 0 , we get a = 1 , b = - 6 , c = k
Now , ? + ? = ( - b/a ) = 6
? + ? = 6 and 3? + 2? = 20
On solving ,
? ? = 4, ? = 2
Product of the roots = k
So, k = ?? = 4 × 2 = 8.
Hence , required answer will be option A .
- 10. The positive value of m for which the roots of the equation 12x2 + mx + 5 = 0 are in the ratio 3 : 2 is :
Options- A. 5?10
- B. 5 ?10 2
- C. 5 12
- D. 12 5 Discuss
Correct Answer: 5?10
Explanation:
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