Discussion
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- Question
- For what value of k the quadratic polynomial 3z2 + 5z + k can be factored into product of real linear factors?
Options- A. k ? 25 6
- B. k ? 25 12
- C. k ? 25 12
- D. k ? 25 6
- Correct Answer
- k ? 25 12
Explanation
- 1. If ? and ? are the roots of the quadratic equation ax 2 + bx + c = 0, the value of ?3 + ?3 is
Options- A. b (b2 - 3ac ) a 3
- B. b ( 3ac - b2 ) a 3
- C. b ( 3ac + b2 ) a 3
- D. None of these Discuss
- 2. The roots of the equation a2x2 - 3abx + 2b2 = 0 are
Options- A. 2b , - b a a
- B. 2b , b a a
- C. - 2b , - b a a
- D. None of these Discuss
- 3. ?. 17x 2 + 48x = 9
?.13y 2 = 32y ?12
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 4. ?. 16x 2 + 20x + 6 = 0
?.10y 2 + 38y + 24 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 5. ?. 8x 2 + 6x = 5
?. 12y 2 ? 22y + 8 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. Find the value of ?30 + ?30 + ?30 +........
Options- A. 5
- B. 3?10
- C. 6
- D. 7 Discuss
Quadratic Equation problems
Search Results
Correct Answer: b ( 3ac - b2 ) a 3
Explanation:
Correct Answer: 2b , b a a
Explanation:
Correct Answer: 1
Explanation:
Correct Answer: 2
Explanation:
Correct Answer: 3
Explanation:
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: 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: 2x2 - 5x + 2 = 0
Explanation:
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: 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 .
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