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- Question
- 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
- Correct Answer
- 11, ?5
ExplanationGiven 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. - 1.
The solution of 2 - x = x - 2 would include : x
Options- A. ?2, ?1
- B. 2, ?1
- C. ?4, 2
- D. 4, ?2 Discuss
- 2. 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 Discuss
- 3. 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
- 4. 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
- 5.
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
- 6. 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
- 7. 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
- 8. 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
- 9. The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m2, find the length of the plot.
Options- A. 22 m
- B. 18 m
- C. 20 m
- D. None of these Discuss
- 10. The value of x in the equation
( x + 1 ) 2 - 3 ( x - 1 ) = 4 is : x 2 x
Options- A. -2
- B. 1 2
- C. -1
- D. 0 Discuss
Quadratic Equation problems
Search Results
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: 10, 6
Explanation:
Let 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 .
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: 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.
Correct Answer: 20 m
Explanation:
Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
? Area = Length × Breadth = x(x + 8)m2 But the area of the plot is given to be 308 m2
? x( x + 8 ) = 308 ? x2 + 8x - 308 = 0
? x2 + 22x - 14x - 308 = 0
? x( x + 22 ) - 14 ( x - 22 ) = 0
? ( x + 22 ) ( x - 14 ) = 0
? x = 14, -22
But, x = ?22 is not possible, since breath cannot be negative
? x = 14
Hence the breadth of the rectangular plot = 14 m Length of the rectangular plot = (14 + 8) m = 22 m.
Correct Answer: -1
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