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- Question
- 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
- Correct Answer
- 20 m
ExplanationLet, 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. - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5.
The solution of 2 - x = x - 2 would include : x
Options- A. ?2, ?1
- B. 2, ?1
- C. ?4, 2
- D. 4, ?2 Discuss
- 6. 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
- 7. If x 2 - 3x + 1 = 0, find the value of x + 1/x,
Options- A. 0
- B. 3
- C. 2
- D. 1 Discuss
- 8. If one of the roots of quadratic equation 7y 2 - 50y + k = 0 is 7, then what is the value of k?
Options- A. 7
- B. 1
- C. 50/7
- D. 7/50 Discuss
- 9. For what value of k, the equation x 2 + 2(k - 4) x + 2k = 0 has equal roots?
Options- A. 6 and 4
- B. 8 and 2
- C. 10 and 4
- D. 12 and 2 Discuss
- 10. The quadrictic equation whose roots are 3 and -1, is
Options- A. x2 - 4x + 3 = 0
- B. x2 - 2x - 3 = 0
- C. x2 + 2x - 3 = 0
- D. x2 + 4x + 3 = 0 Discuss
Quadratic Equation problems
Search Results
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: 17x2 - 20x + 3 = 0
Explanation:
Correct Answer: 4
Explanation:
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: 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: -1
Correct Answer: 3
Explanation:
Given equation is
x2 - 3x + 1 = 0 ? x2 + 1 = 3x
? x2 + 1/x = 3
? x2/x + 1/x = 3
? x + 1/x = 3
Correct Answer: 7
Explanation:
Given quadratic equation is
7y2 - 50y + k = 0
If one root is 7, then it will satisfy the equation i.e putting y = 7 in equation
7 x (7)2 - 50 x 7 + k = 0
? 7 x 49 - 350 + k = 0
? 343 - 350 + k = 0
? k = 7
Correct Answer: 8 and 2
Explanation:
Given equation is
x2 + 2(k - 4)x + 2k = 0
On comparing with ax2 + bx + c = 0
Here, a = 1, b = 2(k -4), c = 2k
Since, the root are equal, we have D = 0.
b2 - 4ac = 0
? 4(k - 4)2 - 8k = 0
4(k2 + 16 - 8k) - 8k = 0
? 4k2 + 64 - 32k - 8k = 0
? 4k2 - 40k + 64 = 0
? k2 - 10k + 16 = 0
? k2 - 8k - 2k + 16 = 0
? k(k - 8) -2 (k - 8) = 0
? (k - 8) (k - 2) = 0
Hence, the value of k 8 or 2.
Correct Answer: x2 - 2x - 3 = 0
Explanation:
Given that, the roots of the quadrictic equation are 3 and -1.
Let ? = 3 and ? = -1
Sum of roots = ? + ? = 3 - 1 = 2
Products of roots = ? . ? = (3) (-1) = -3
? Required quadric equation is
x2 - (? + ?)x + ? ? = 0
? x2 - (2)x + (-3) = 0
? x2 - 2x - 3 = 0
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