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- Question
- The sum of the squares of 2 natural consecutive odd numbers is 394. The sum of the numbers is :
Options- A. 24
- B. 32
- C. 40
- D. 28
- Correct Answer
- 28
ExplanationLet, the two natural consecutive odd numbers be n and (n + 2)
Now, according to the question,
? n2 + ( n + 2 )2 = 394
? n2 + n2 + 4 + 4n = 394
? 2n2 + 4n - 390= 0
? n2 + 2n - 195 = 0
? n2 + 15n - 13n - 195 = 0
? n( n + 15 ) - 13( n + 15 ) = 0
? ( n + 15 ) ( n - 13 ) = 0
? n = 13 and n ? - 15
? The two natural consecutive odd numbers be 13 and (13 + 2) = 15 .
? the sum of the numbers = 13 + 15 = 28
Quicker Approach:
By mental operation, 132 + 152 = 169 + 225 = 394
? Required sum = 13 + 15 = 28 - 1. Find the value of ?30 + ?30 + ?30 +........
Options- A. 5
- B. 3?10
- C. 6
- D. 7 Discuss
- 2. The factors of ( a2 + 4b2 + 4b ? 4ab ? 2a ? 8 ) are :
Options- A. (a ? 2b ? 4) (a ? 2b + 2)
- B. (a ? b + 2) (a + 4b + 4)
- C. (a + 2b ? 4) (a + 2b + 2)
- D. (a + 2b ? 1) (a ? 2b + 1) Discuss
- 3. If ?, ? are the roots of the equation 2x2 - 3x + 1 = 0, form an
equation whose roots are ? and ? ? ?
Options- A. 2x2 + 5x + 2 = 0
- B. 2x2 - 5x - 2 = 0
- C. 2x2 - 5x + 2 = 0
- D. None of these Discuss
- 4. Find 2 consecutive positive odd integers whose squares have the sum 290.
Options- A. 11, 13
- B. 13, 15
- C. 9, 11
- D. None of these Discuss
- 5. The roots of the equation x2 + px + q = 0 are equal if :
Options- A. p2 = 2q
- B. p2 = 4q
- C. p2 = - 4q
- D. p2 = - 2q Discuss
- 6. The roots of the equation ax2 + bx + c = 0 will be reciprocal if
Options- A. a = b
- B. b = c
- C. c = a
- D. None of these Discuss
- 7. ?. x 2 ? 4 = 0
?. y 2 + 6y + 9 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 8. ?. x 2 = 729
?. y = ? 729
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9. ?. 2x 2 + 11x + 14 = 0
?. 4y 2 + 12y + 9 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 10. ?. x 2 - 7x + 12 = 0
?. y 2 - 12y + 32 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Quadratic Equation problems
Search Results
Correct Answer: 6
Explanation:
According to question ,we can say that
Let , x = ?30 + ?30 + ?30 +........
On squaring both sides, we have
x2 = 30 + ?30 + ?30 + ?30 +........
? x2 = 30 + x ? x2 - x - 30 = 0
? x2 - 6x + 5x - 30 = 0
? x( x - 6 ) + 5( x - 6 ) = 0
? ( x - 6 ) ( x + 5 ) = 0
? x = 6 because x ? - 5
Hence , required answer is 6 .
Correct Answer: (a ? 2b ? 4) (a ? 2b + 2)
Explanation:
Given that :- The factors of a2 + 4b2 + 4b ? 4ab ? 2a ? 8
= a2 + 4b2 ? 4ab ? 2a + 4b ? 8
= (a ? 2b) 2 ? 2(a ? 2b) ? 8
Let, (a ? 2b) = x
? The given expression = x2 ? 2x ? 8
= x2 ? 4x + 2x ? 8
= x(x ? 4) + 2(x ? 4)
= (x ? 4) (x + 2)
Putting the value of x , we get
? a2 + 4b2 + 4b ? 4ab ? 2a ? 8 = (a ? 2b ? 4) (a ? 2b + 2)
Therefore , required answer will be (a ? 2b ? 4) (a ? 2b + 2) .
Correct Answer: 2x2 - 5x + 2 = 0
Explanation:
Correct Answer: 11, 13
Explanation:
According to question ,
Let, the two consecutive odd positive integers be 2x + 1 and 2x + 3 where x is a whole number.
Now, ( 2x + 1 )2 + ( 2x + 3 )2 = 290
? 4x2 + 4x + 1 + 4x2 + 12x + 9 = 290
? 8x2 + 16x - 280 = 0
? x2 + 2x - 35 = 0
? ( x + 7 ) ( x - 5 ) = 0
? x = 7, - 5
But, x = ?7 is not possible, since ?7 is not a whole number .
? x = 5.
We get , 2x + 1 = 2 x 5 + 1 = 11 and 2x + 3 = 2 x 5 + 3 = 13
Thus , two consecutive positive odd integers are 11 and 13 .
Correct Answer: p2 = 4q
Explanation:
On comparing it with ax2 + bx + c = 0 , we get a = 1, b = p, c = q
The roots of the equation x2 + px + q = 0 are equal if
b2 - 4ac = 0
? p2 - 4q = 0 ? p2 = 4q.
Thus , required answer is option B .
Correct Answer: c = a
Explanation:
Correct Answer: 1
Explanation:
According to question ,we have
From equation ?. x2 ? 4 = 0
? x = ± 2,
From equation ?. y2 + 6y + 9 = 0
? ( y + 3 )2 = 0
? ( y + 3 )( y + 3 ) = 0
? y + 3 = 0 ? y = -3 , -3
Clearly , x > y is required answer .
Correct Answer: 4
Explanation:
According to question ,we have
From equation ?. x2 = 729
? x = ± ?729 = ± 27
From equation ?. y = ?729
? y = 27
Hence , x ? y is required answer .
Correct Answer: 3
Explanation:
Correct Answer: 4
Explanation:
As per the given above equations , we have
From equation ?. x2 - 7x + 12 = 0
? x2 - 4x - 3x + 12 = 0
? x( x - 4) - 3( x - 4) = 0
? ( x - 4) ( x - 3) = 0
? x = 4 or, 3
?. y2 - 12y + 32 = 0
? y2 - 8y - 4y + 32 = 0
? y( y - 8) - 4( y - 8) = 0
? ( y - 8) ( y - 4) = 0
? y = 4 or, 8
Thus , x ? y is required answer .
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