Discussion
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- Question
- If 2x 2 - 7xy + 3y 2 = 0, then the value of x : y is
Options- A. 3 : 2
- B. 2 : 3
- C. 3 : 1 and 1 : 2
- D. 5 : 6
- Correct Answer
- 3 : 1 and 1 : 2
Explanation2x2 - 7xy + 3y2 = 0
? 2x2 - 6xy - xy + 3y2 = 0
? 2x(x - 3y) - y(x - 3y) = 0
? (2x - y) (x - 3y) = 0
Either, 2x - y = 0 ? 2x = y
? x/y = 1/2
or x - 3y = 0
? x = 3y ? x/y = 3/1 - 1. If [a + (1/a)] 2 = 3 , what is the value of a 3 + (1/a) 3?
Options- A. 10?3/3
- B. 0
- C. 3?3
- D. 6?3 Discuss
- 2. Find the roots of the equation 2x 2 - 11x + 15 = 0
Options- A. 3 and 5/2
- B. -3 and -5/2
- C. 5 and 3/2
- D. -5 and -3/2 Discuss
- 3. If one root of x 2 - 6kx + 5 = 0 is 5, find the value of k.
Options- A. -1/2
- B. -1
- C. 1
- D. 2 Discuss
- 4. Find the roots of the equation 2x 2 - 9x - 18 = 0.
Options- A. 3/2 and 6
- B. -3/2 and - 6
- C. -3/2 and 6
- D. 3/2 and -6 Discuss
- 5. Which of the following equations has real roots?
Options- A. 2x2 - 3x + 4 = 0
- B. (x - 1) (2x - 5) = 0
- C. 3x2 + 4x + 5 = 0
- D. Cannot be determined Discuss
- 6. If one roots of the equation x 2/a = x/b + 1/c = 0 is reciprocal of the other, then which one of the following is correct?
Options- A. a = b
- B. b = c
- C. ac = 1
- D. a = c Discuss
- 7. One root of the quadratic equation x2 - 5 x + 6 = 0 is 3. Find the other root.
Options- A. 2
- B. ?2
- C. 1
- D. ?1 Discuss
- 8. Construct a quadratic equation whose roots have the sum = 6 and product = ?16.
Options- A. x2 - 6x - 16 = 0
- B. x2 + 6x - 16 = 0
- C. x2 - ?3x - 16 = 0
- D. None of these Discuss
- 9. ?. 4x + 7y = 209
?. 12x ? 14y = ? 38
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 10. ?. 18x 2 + 18x + 4 = 0
?. 12y 2 + 29y + l4 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Quadratic Equation problems
Search Results
Correct Answer: 0
Explanation:
[a + (1/a)]2 = 3
Taking square roots both sides, we get
a + (1/a) = ?3
On cubing both sides, we
[a + (1/a)]3 = (?3)3
? a3 + 1/a3 + 3.a.1/[a(a + 1/a)] = 3 ?3
? a3 + 1/a3 + 3?3 = 3?3
? a3 + 1/a3 = 0
Correct Answer: 3 and 5/2
Explanation:
2x2 -11x + 15 = 0
[by factorisation method]
? 2x2 - (6x + 5x) + 15 = 0
? 2x2 - 6x - 5x + 15 = 0
? 2x(x - 3) - 5 (x - 3) = 0
? (2x - 5) (x - 3) = 0
? x = 5/2, 3
Hence, the roots are 5/2 and 3.
Correct Answer: 1
Explanation:
Given, one root of x2 - 6kx + 5 = 0 is 5.
? x = 5 satisfies x2 - 6kx + 5 = 0
? 52 - 30k + 5 = 0
? 25 - 30k + 5 = 0
? 30 - 30k = 0
? 30k = 30
? k = 1
Correct Answer: -3/2 and 6
Explanation:
Given equation is 2x2 - 9x - 18 = 0
[by factorisation method]
? 2x2 - 12x + 3x - 18 = 0
? 2x(x - 6) + 3(x - 6) = 0
? (2x + 3) (x - 6) = 0
? x = -3/2, 6
Correct Answer: (x - 1) (2x - 5) = 0
Explanation:
(x - 1) (2x - 5) = 0 ? x = 1, 5/2
So, its roots are real.
Correct Answer: a = c
Explanation:
Given quadric equation is
x2 + x/b + 1/c = 0 ...(i)
Now, by condition the roots of the Eq.(i) are ? and 1/?.
Now,product of roots = (1/c) / (1/a)
? ?.(1/?) = a/c
? c = a
which is the required relation.
Correct Answer: 2
Explanation:
The given equation is
x2 - 5x + 6 = 0 ? x 2 - 2x - 3x+ 6 = 0
? x( x - 2 ) - 3( x - 2 ) = 0
? ( x - 2 ) ( x - 3 ) = 0
? x - 2 = 0 or x - 3 = 0
? x = 2 or x = 3
Thus, the other root of the given quadratic equation is 2.
Correct Answer: x2 - 6x - 16 = 0
Explanation:
Given that :- sum of the roots = 6
And Product of two roots = -16
The required quadratic equation is x2 ? (sum of the roots) x + (product of the roots) = 0
? x2 - 6x - 16 = 0
Correct Answer:
Explanation:
According to question ,we can say that
?. 4x + 7y = 209 ...............( 1 )
?. 12x ? 14y = ? 38 .................... ( 2 )
Multiplying (1) by (2):
8x + 14y = 418 ................(3)
Adding (2) and (3):
20x = 380 ? x = 19
Substituting the value of x in (1), we get
76 + 7y = 209
? 7y = 133 ? y = 19
From above equations it is clear that x = y is correct answer .
Correct Answer: 4
Explanation:
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