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- Question
- 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
- Correct Answer
- 3 and 5/2
Explanation2x2 -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. - 1. 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
- 2. 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
- 3. 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
- 4. Which of the following equations is a quadratic?
Options- A. x3 - x2 - x + 5 = 0
- B. x4 - 10
- C. 7x2 = 49
- D. x4 - x3 = 9000 Discuss
- 5. In a two-digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is
Options- A. 47
- B. 59
- C. 23
- D. 35 Discuss
- 6. 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
- 7. 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 Discuss
- 8. 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
- 9. 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
- 10. 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
Quadratic Equation problems
Search Results
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: 7x2 = 49
Explanation:
Clearly, 7x2 = 49 or 7x2 - 49 = 0, which is of the form ax2 + bx + c = 0, where b = 0.
Thus, 7x2 - 49 = 0 is a quadratic equation.
Correct Answer: 47
Explanation:
let us assume the ten's digit number be x and unit's place digit be y.
Then two digit Original Number = 10x + y
According to question ? y = 2x - 1 ................(1)
When digits are interchanged then new number = 10y + x
If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20,
New Number - Original Number = Original number - 20
? 10y + x - (10x + y) = 10x + y - 20
? 10y + x - 10x - y - 10x - y = - 20
? 8y - 19x = - 20
? 19x - 8y = 20 ...................(2)
Put the value of y from equation (1) in above equation (2).
? 19x - 8(2x - 1) = 20
? 19x - 16x - 8 = 20
? 7x = 20 + 8
? 7x = 28
? x = 28/7
? x = 4
Put the value of y in equation (1)
From (i) y = 2 x 4 -1 = y = 7
? original number = 10x + y =10 x 4 + 7 = 47.
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 : 1 and 1 : 2
Explanation:
2x2 - 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
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
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