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- Question
- ?. 24x 2 + 38x + 15 = 0
?.12y 2 + 28y + 15 = 0
Options- A. x ? y
- B. x > y
- C. x ? y
- D. x < y
- Correct Answer
- x ? y
Explanation
- 1. ?. 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
- 2. ?. 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
- 3. ?. 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
- 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
- 5. 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
- 6. 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
- 7. 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
- 8. If ?, ? are the roots of the equation x2 + kx + 12 = 0 such that ? ? ? = 1, the value of k is
Options- A. 0
- B. ± 5
- C. ± 1
- D. ± 7 Discuss
- 9. Determine k such that the quadratic equation x2 - 2( 1 + 3k ) x + 7 ( 3 + 2k ) = 0 has equal roots.
Options- A. 2, - 10 9
- B. 2, 10 9
- C. - 2, 10 9
- D. - 2, -10 9 Discuss
- 10. If ? and ? are the roots of the equation x2 - 3?x + ?2 = 0,
find ? if ?2 + ?2 = 7 4
Options- A. ± 1 2
- B. ± ?7 2
- C. ± ?3 2
- D. None of these Discuss
Quadratic Equation problems
Search Results
Correct Answer: Relationship between x and y cannot be established
Explanation:
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 .
Correct Answer:
Explanation:
Correct Answer: x < y
Explanation:
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.
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 .
Correct Answer: 5?10
Explanation:
Correct Answer: ± 7
Explanation:
As per the given above question , we know that
Let, ?, ? be the roots of the equation x2 + kx + 12 = 0
? ? + ? = ?k and ?? = 12
Now ( ? - ? )2 = ( ? + ? )2 - 4??
( 1 )2 = k2 - 4(12)
? k2 = 49 ? k = ± 7.
Correct Answer: 2, - 10 9
Explanation:
Correct Answer: ± 1 2
Explanation:
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