Discussion
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- Question
- Divide 16 into 2 parts such the twice the square of the larger part exceeds the square of the smaller part by 164.
Options- A. 10, 6
- B. 8, 8
- C. 12, 4
- D. None of these
- Correct Answer
- 10, 6
ExplanationLet the smaller part be x. Then the larger part = 16 ? x.
According to question , we have
2( larger part )2 - ( smaller part )2 = 164
Now , 2( 16 - x )2 - x2 = 164
? 2( 256 + x2 - 32x ) - x2 = 164
? x2 - 64x + 348 = 0
? x2 - 6x - 58x + 348 = 0
? x(x - 6) - 58(x - 6) = 0
? (x - 6) (x - 58)
x = 6 or x = 58
But m = 58 is not possible, since sum of the two parts is 16
? smaller part ( x ) = 6,
? other part = 16 - x = 16 - 6 = 10.
Hence , required answer will be option A . - 1. The common root of the equations x2 - 7x + 10 = 0 and x2 - 10x + 16 = 0 is :
Options- A. - 2
- B. 3
- C. 5
- D. 2 Discuss
- 2. The expression x4 + 7x2 + 16 can be factored as :
Options- A. (2 + x + 1) (2 + x + 16)
- B. (2 + x + 1) (2 ? x + 16)
- C. (2 + x + 4) (2 ? x + 4)
- D. (2 + x ? 4) (2 ? x ? 4) Discuss
- 3.
One root of the equation 3x2 - 10x + 3 = 0 is 1 . Find the other root. 3
Options- A. 3
- B. 1 3
- C. - 3
- D. None of these Discuss
- 4. x = 3a solution of the equation 3x2 + (k ? 1)x + 9 = 0 if k has value
Options- A. 13
- B. ?13
- C. 11
- D. ?11 Discuss
- 5. The equation x2 ? px + q = 0, p, q ? R has on real root if :
Options- A. p2 ? 4q
- B. p2 < 4q
- C. p2 > 4q
- D. None of these Discuss
- 6.
The solution of 2 - x = x - 2 would include : x
Options- A. ?2, ?1
- B. 2, ?1
- C. ?4, 2
- D. 4, ?2 Discuss
- 7. If log10 ( x2 - 6x + 45 ) = 2, then the values of x are
Options- A. 6, 9
- B. 9, ?5
- C. 10, 5
- D. 11, ?5 Discuss
- 8. If the equations x2 + 2x - 3 = 0 and x2 + 3x - k = 0 have a common root, then the non - zero value of k is :
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 9. Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x +17 = 0
Options- A. 17x2 - 20x + 3 = 0
- B. 17x2 + 20x + 3 = 0
- C. 17x2 - 20x - 3 = 0
- D. None of these Discuss
- 10. The expression x2 ? x + 1 has :
Options- A. one proper linear factor
- B. two proper linear factors
- C. no proper linear factor
- D. None of these Discuss
Quadratic Equation problems
Search Results
Correct Answer: 2
Explanation:
As per the given above question , we can say that
The given quadratic equations are
x2 - 7x + 10 = 0 ? (x ? 5)(x ? 2) = 0 ? x = 5, 2
And x2 - 10x + 16 = 0 ? (x ? 8)(x ? 2) = 0 ? x = 8, 2
? Common root is 2.
Correct Answer: (2 + x + 4) (2 ? x + 4)
Explanation:
The given expression x4 + 7x2 + 16 = ( x4 + 8x2 + 16 ) - x2
= ( x4 + 2 * 4 * x2 + 42 ) - x2
= ( x2 + 4 )2 - x2
= ( x2 + 4 + x ) ( x2 + 4 - x )
Hence , x4 + 7x2 + 16 = ( x2 + x + 4 ) ( x2 - x + 4 ).
Option C is correct answer .
Correct Answer: 3
Explanation:
Correct Answer: ?11
Explanation:
The given quadratic equation 3x2 + (k ? 1)x + 9 = 0
Putting x = 3 in above given eq. , we get
27 + 3(k ? 1) + 9 = 0
? 27 + 3k - 3 + 9 = 0
? 3k = ?33 ? k = ?11.
Hence , the value of k is ?11.
Correct Answer: p2 < 4q
Explanation:
According to question , we can say that
The equation x2 ? px + q = 0, p, q ? R has no real root
On comparing with quadratic eq. Ax2 + Bx + C = 0 , we get
? A =1, B= - p, C = q
Now ,we have B2 < 4AC
? ( - P )2 < 4 x 1 x q
? p2 < 4q.
Hence , option B is correct answer .
Correct Answer: 2, ?1
Explanation:
Given equation is
2x - x2 = x - 2 ? x2 - x - 2 = 0
? ( x + 1 ) ( x - 2 ) = 0
? x = 2 or = - 1.
Therefore , option B is correct answer .
Correct Answer: 11, ?5
Explanation:
Given that : - log10 ( x2 - 6x + 45 ) = 2
? x2 - 6x + 45 = 102 = 100
? x2 - 6x - 55 = 0
? ( x - 11 ) ( x + 5 ) = 0
? x = 11 or x = - 5.
Hence , the values of x are 11 and - 5.
Correct Answer: 4
Explanation:
Correct Answer: 17x2 - 20x + 3 = 0
Explanation:
Correct Answer: no proper linear factor
Explanation:
According to question , we have
Comparing x2 - x + 1 with ax2 + bx + c , we get
a = 1, b = ?1, c = 1
Here D = b2 - 4ac = ( - 1 )2 - 4 (1)(1)
= 1 - 4 = - 3
Since D < 0, so the given expression has no proper linear factor.
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