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- Question
- The quadratic equation with rational coefficients, whose one root is ?5, is :
Options- A. x 2 + 5 = 0
- B. x 2 - 10 = 0
- C. x 2 - 5 = 0
- D. None of these
- Correct Answer
- x 2 - 5 = 0
ExplanationAs per the given above question , we have
Let k1 and k2 be the roots of quadratic equation .
One root is k1 = ?5
So the other root is k2 = ? ?5
? Sum of the roots = k1 + k2 = ?5 + ( -?5 ) = 0
and product of the roots = k1 × k2 = ? (?5) (- ?5) = ?5
? Required equation is x2 - (sum of the roots)x + (product of the roots) = 0
? x2 - 5 = 0. - 1. Mr. Arjun is on tour and he has ? 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by ? 3. For how many days is Mr. Arjun out on tour?
Options- A. 40
- B. 20
- C. 60
- D. 15 Discuss
- 2. (4/? x) + (7/? x) = ? x;
y 2 - (11) 5/2/? y = 0
Options- A. if x > y
- B. if x ? y
- C. if x < y
- D. if x ? y Discuss
- 3. x 2 - 365 = 364; y - ? 324 = ? 81
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 4. 3x 2 + 8x + 4 = 0; 4y 2 - 19y + 12 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 5. x 2 - x - 12 = 0; y 2 + 5y + 6 = 0
Options- A. If x > y
- B. If x ? y
- C. If x < y
- D. If x ? y Discuss
- 6.
The roots of x + 4 + x - 4 = 10 are : x - 4 x + 4 3
Options- A. ± 4
- B. ± 6
- C. ± 8
- D. 2 ± ?3 Discuss
- 7. ?. x 2 ? 19x + 84 = 0
?. y 2 ? 25y + 156 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 8.
?. 12 - 23 = 5?x ? x ? x
?. ? y - 5 ? y = 1 12 12 ? y
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9.
?. 9 + 19 = ?x ? x ? x
?. y5 - ( 2 × 14 ) 11/2 = 0 ? y
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 10. ?. ? 784x + 1234 = 1486
?. ? 1089y + 2081 = 2345
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Quadratic Equation problems
Search Results
Correct Answer: 20
Explanation:
Let Mr . Arjun is on tour for N days.
Then, according to the question,
Difference in expenses per day for original and extended tour = 3
360/N - 360/(N + 4) = 3
? 1/N - 1/(N + 4) = 3/360 = 1/120
? [N + 4 - N] / [ N x (N + 4)] = 1/120
? N(N + 4) = 4 x 120 = 480
? N2 + 4N - 480 = 0
? N2 + 24 - 20x - 480 = 0
? N(N + 24) - 20(N + 24) = 0
? (N + 24) (N - 20) = 0
? N = 20
(we ignore -ve value of x, that is, -24 because days cannot be negative)
Correct Answer:
Explanation:
4/?x + 7/?x = ?x;
? 11/?x = ?x
? x = 11
and y2 - (11)5/2/?y = 0
? y2 = (11)5/2/(y)1/2
? y2 x y1/2 = (11)5/2
? (y)5/2 = (11)5/2
? y = 11
? x = y
Correct Answer: If x ? y
Explanation:
x2 - 365 = 364
? x2 = 364 + 365
? x = ?729 = ± 27
and y - ?324 = ?81 ? y - 18 = 9
? y = 27
So, y ? x or x ? y because y = 27 and x = 27 and - 27.
Correct Answer: If x < y
Explanation:
3x2 + 8x + 4 = 0
? 3x2 + 6x + 2x + 4 = 0
? 3x(x + 2) + 2(x + 2) = 0
? (x + 2) (3x + 2) = 0
? x = - 2, - 2/3
and 4y2 - 19y + 12 = 0
? 4y2 - 16y - 3y + 12 = 0
? 4y(y - 4) -3(y - 4) = 0
? (y - 4) (4y - 3) = 0
? y = 4, 3/4
Hence, y > x or x < y
Correct Answer: If x ? y
Explanation:
x2 - x - 12 = 0
? x2 - 4x + 3x - 12 = 0
? x(x - 4) + 3 (x - 4) = 0
? (x - 4) (x + 3) = 0
? x = - 3, 4
and y2 + 5y + 6 = 0
? y2 + 3y + 2y + 6 = 0
? y(y + 3) + 2(y + 3) = 0
? (y + 3) (y + 2) = 0
? y = - 3, - 2
? x ? y
[? x = - 3 and y = - 3, so x = y and x = 4 and y = - 2, hence x > y]
Correct Answer: ± 8
Explanation:
Correct Answer: 4
Explanation:
According to question ,we can say that
From equation ?. x2 ? 19x + 84 = 0
? x2 ? 7x ? 12x + 84 = 0
? (x ? 7)(x ? 12) = 0
? x = 7, 12
From equation ?. y2 ? 25y + 156 = 0
? y2 ? 13y ? 12y + 156 = 0
? (y ? 13)(y ? 12) = 0
? y =12, 13
? x ? y
From above it is clear that x ? y is correct answer .
Correct Answer: 1
Explanation:
Correct Answer:
Explanation:
Correct Answer: 1
Explanation:
According to question ,we can say that
From equation ?. ?784x + 1234 = 1486
? ?784x = 252
? 28x = 252
? x = 9
From equation ?. ?1089y + 2081 = 2345
? ?1089y = 264
? 33y = 264
? y = 8
? x > y
Thus , required answer will be x > y .
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