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- Question
- 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
- Correct Answer
- 8 and 2
ExplanationGiven 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. - 1. 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
- 2. If x 2 - 3x + 1 = 0, find the value of x + 1/x,
Options- A. 0
- B. 3
- C. 2
- D. 1 Discuss
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. If ? and ? are the roots of the equation 4x 2 - 19x + 12 = 0, find the equation having the roots 1/? and 1/?
Options- A. 4x2 + 19 + 12 = 0
- B. 12x2 - 19x + 4 = 0
- C. 12x2 + 19x + 4 = 0
- D. 4x2 + 19x - 12 = 0 Discuss
- 8. The difference in the roots of the equation 2x 2 - 11x + 5 = 0 is
Options- A. 4.5
- B. 4
- C. 3.5
- D. 3 Discuss
- 9. If {2 1/ 4} is the solution set of a quadric equation, find that equation .
Options- A. 4x2 - 9x + 2 = 0
- B. 2x2 - 9x + 4 = 0
- C. x2 -18x - 6 = 0
- D. 2x2 - 18x + 3 = 0 Discuss
- 10. If p and q are the roots of the equation x 2 + px + q = 0, then
Options- A. p = 1 and q = -2
- B. p = 0 and q = 1
- C. p = -2 and q = 0
- D. p = -2 and q = 1 Discuss
Quadratic Equation problems
Search Results
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: 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: -1
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: 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: 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
Correct Answer: 12x2 - 19x + 4 = 0
Explanation:
Given equation is 4x2 - 19x + 12 = 0
Let given equation having the roots 1/? and 1/?,
Then required equuation is
12x2 - 19x + 4 = 0
Correct Answer: 4.5
Explanation:
Let ? and ? be the roots of the quadratic equation 2x2 - 11x + 5 = 0
? ? + ? = -(-11)/2 = 11/2 ...(i)
and ?? = 5/2
Now, (? - ?)2 = (? + ?)2 - 4??
= (11/2)2 - 4(5/2) = 121/4 - 20/2
= 121 - 40/4 = 81/4 = (9/2)2
? Difference of roots = (? - ?) = 9/2 = 4.5
Correct Answer: 4x2 - 9x + 2 = 0
Explanation:
Let ? = 2, ? = 1/4
Then, ? + ? = 2 + 1/4 = 9/4
?? = 2.1/4 = 1/2
Equation having the roots ? and ? is
x2 - (? + ?)x + ? ? = 0
? x2 - 9/4x + 1/2 = 0
? 4x2 - 9x + 2 = 0
Correct Answer: p = 1 and q = -2
Explanation:
Since, p and q are the roots of the equation x2 + px + q = 0
Then, p + q = - p
and pq = q
Now, pq = q
? p = 1
Putting the value of p in p + q = - p, we get
1 + q = - 1
? q = - 2
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