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Home ‣ Aptitude ‣ Quadratic Equation Comments
- Question
- Construct a quadratic equation whose roots are ?2 and 2 ?2
Options- A. x 2 - 3?2x - 4 = 0
- B. x 2 - 3?2x + 4 = 0
- C. x 2 + 3?2x - 4 = 0
- D. x 2 + 3?2x + 4 = 0
- Correct Answer
- x 2 - 3?2x + 4 = 0
ExplanationLet k1 and k2 be the roots of quadratic equation .
Given :- k1 = ?2 and k2 = 2 ?2
Sum of the roots = ?2 + 2 ?2 = 3 ?2
Product of the roots = ( ?2 ) ( 2?2 ) = 4
Hence the required quadratic equation is x 2 = (sum of the roots) x + (Product of two roots) = 0
? x 2 - 3 ?2x + 4 = 0. - 1. If ? and ? are the roots of the quadratic equation ax2 + bx + c = 0, then the value of
? + ? is ? ?
Options- A. b 2 - 2ac ac
- B. b 2 - 2ac 2ac
- C. b 2 - ac 2ac
- D. b 2 + 2ac ac Discuss
- 2. Determine p so that the equation x 2 + 5px + 16 = 0 has on real root.
Options- A. - 4 < p < 4 . 5 5
- B. - 8 < p < 8 . 5 5
- C. p < - 4 or p > 4 5 5
- D. None of these Discuss
- 3. Form a quadratic equation whose one root is 3 - ?5 and the sum of roots is 6
Options- A. x2 ? 6x + 4 = 0
- B. x2 + 6x + 4 = 0
- C. x2 ? 6x ? 4 = 0
- D. None of these Discuss
- 4. ? 6 + ?6 + ?6 +........ is equal to
Options- A. 2
- B. 5
- C. 4
- D. 3 Discuss
- 5. ?. ? 500x + ? 402 = 0
?. ? 360y + ( 200 ) 1/2 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 6. ?. 16x 2 + 20x + 6 = 0
?. 10y 2 + 38y + 24 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 7. ?. 18x 2 + 18x + 4 = 0
?. 12y 2 + 29y + 14 =0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 8. ?. 4x + 7y = 209
?. 12x ? 14y = ?38
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9. ?. 17x 2 + 48x = 9
?. 13y 2 = 32y ? 12
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 10. ?. 8x 2 + 6x = 5
?. 12y 2 ? 22y + 8 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Quadratic Equation problems
Search Results
Correct Answer: b 2 - 2ac ac
Explanation:
Correct Answer: - 8 < p < 8 . 5 5
Explanation:
Correct Answer: x2 ? 6x + 4 = 0
Explanation:
Given : - Sum of the roots ( k1 + k2 ) = 6
One root k1 = 3 - ?5
? the other root k2 = 6 - ( 3 - ?5) = 3 + ?5
? Product of roots k1k2 = ( 3 - ?5 ) ( 3 + ?5 )
product of roots = 9 - 5 = 4
Hence , the required equation is x2 - (sum of the roots)x + (product of roots) = 0
? x2 - 6x + 4 = 0.
Correct Answer: 3
Explanation:
As per the given above question , we have
Let, x = 6 + ?6 + ?6 + ?6 +........
On squaring both sides, we have
x2 = 6 + ?6 + ?6 + ?6 +........
? x2 = 6 + x
? x2 - x - 6 = 0
? x2 - 3x + 2x - 6 = 0
? x( x - 3 ) + 2( x - 3 ) = 0
? ( x - 3 ) ( x + 2 ) = 0
? x = 3 and x ? ?2 because numbers are positive.
Thus , correct answer will be 3 .
Correct Answer: 3
Explanation:
As per the given above equations , we can say that
?.
?500x + ?402 = 0
? ?500x = - ?402
? x = - ?( 402/500 ) = - ?( 400/500 ) = - 0.9
?. ?360y + ( 200 )1/2 = 0
? ?360y = - ?200
?
y = - ?( 200 / 360 ) = - 0.74
Clearly, we can see that x < y is required answer .
Correct Answer: 2
Explanation:
Correct Answer: 4
Explanation:
Correct Answer:
Explanation:
Correct Answer: 1
Explanation:
Correct Answer: 3
Explanation:
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