Question 1 1 / -0
Which of the following equations has –84 as discriminant?
Solution
Discriminant = b2 - 4ac 2x2 + 2x + 11 = 0 D = 4 - 4 x 2 x 11 = 4 - 88 = - 84
Question 2 1 / -0
Which of the following equations has
as one of its solutions?
Question 3 1 / -0
Which of the following equations has -2 as one of its solutions?
Solution
(27 + 2)2 = 49 y2 - 2 does not satisfy this (3y + 7)2 = 64 y = - 2 does not satisfy this (y + 1)2 = 2 y = -2 does not satisfy this. (4) option i : e None of these.
Question 4 1 / -0
Which of the following equations is same as 4x2 - 5x - 3 = 0?
Solution
4x
2 - 5x - 3 = 0
x
2 -
-
= 0
= 0
Option (4)
Question 5 1 / -0
Which of the following equations has 8 as one of its solutions?
Solution
(x + 3)2 = 36 x = 8 is not a solution (x - 3)2 = 25 x = 8 gives 52 = 25 25 = 25 Hence x = 8 is a solution to this equation.
Question 6 1 / -0
Which of the following equations has 9 as discriminant?
Solution
x2 + 5x + 4 = 0 d = b2 - 4ac 25 - 4 (4) 1 = 25 - 16 - 9 Option (1)
Question 7 1 / -0
Which of the following equations has real and equal roots?
Solution
3x2 - 17x + 20 = 0 for roots D = 0 D = 289 - 240 = 49 No equal roots. (2) 2x2 - 3x + 5 = 0 D = 9 - 40 = - 31 (3) 9x2 - 24x + 16 = 0 d = 576 - 64 x 9 = 576 - 576 = 0 Hence real and equal roots.
Question 8 1 / -0
Which of the following equations has the solution y = 2?
Solution
(1) (2y + 1)2 = 25 y = 2 satifies this (2) (3y - 1)2 = 25 y = 2 satisfies this (3) (2y + 7)2 = 121 y = 2 satisfies this (4) All of the above.
Question 9 1 / -0
Which of the following equations has no real roots?
Solution
For no real roots D < 0 (1) D = 81 - 80 = 1 > 0 (2) 196 - 4 (8) (-15) > 0 (3) D = 324 - 320 > 0 (4) D = 169 - 220 < 0 Hence (4)
Question 10 1 / -0
What will be the discriminant of the given quadratic equation? 3x2 + 5x + 2 = 0
Solution
3x2 + 5x + 2 = 0 D = 25 - 24 = 1
Question 11 1 / -0
If the roots of the quadratic equation ax2 + bx + c = 0 are real and distinct, then _____.
Solution
ax2 + bx + c = 0 b2 - 4ac > 0
Question 12 1 / -0
What will be the discriminant of the given quadratic equation? 5x2 + x + 7 = 0
Solution
5x2 + x + 7 = 0 D = 1 - 4 x 5 x 7 = - 139
Question 13 1 / -0
Which of the following equations has (2 +
) as one of its solutions?
Solution
(3x - 6)
2 = 90
3x - 6 =
3x - 6 = 3
x = 2 +
Hence (1)
Question 14 1 / -0
What will be the discriminant of the given quadratic equation? 2x2 + 7x + 5 = 0
Solution
2x2 + 7x + 5 = 0 D = 49 - 4 x 2 x 5 = 9
Question 15 1 / -0
If the roots of the quadratic equation ax2 + bx + c = 0 are real and equal, then ______.
Solution
ax2 + bx + c = 0 for equal and real D = 0 D = b2 - 4ac = 0
Question 16 1 / -0
Which of the following equations can be obtained after completing the square of x2 + 6x + 3 = 0?
Solution
x2 + 6x + 3 = 0 (x + 3)2 + 3 - 9 = 0 (x + 3)2 = 6
Question 17 1 / -0
What will be the discriminant of the given quadratic equation? ax2 + bx + c = 0
Question 18 1 / -0
Which of the following equations has no real roots?
Solution
x2 + x + 12 = 0 D = 1 - 4 x (12) = - 47 D < 0 Hence no real root.
Question 19 1 / -0
Which of the following equations can be obtained after completing the square of x2 + 4x + 2 = 0?
Solution
x2 + 4x + 2 = 0 (x + 2)2 + 2 - 4 = 0 (x + 2)2 = 2
Question 20 1 / -0
Which of the following equations has 2
as one of its solutions?
Solution
(x - 2
)
2 = 0
x = 2
satisfy this
Question 21 1 / -0
Which of the following equations can be obtained after completing the square of x2 + 9x + 7 = 0?
Solution
x
2 + 9x + 7 = 0
= 0
Question 22 1 / -0
Which of the following equations has real and distinct roots?
Solution
For real and distinct roots D = b2 - 4ac > 0 (1) 25 - 20 > 0 Real and distinct roots (2) 144 - 16 > 0 Real and distinct roots (3) 25 - 8 > 0 Real and distinct roots All of the above
Question 23 1 / -0
Which of the following equations has
as one of its solutions?
Solution
(2x + 3)
2 = 100
= 100
(7 + 3)
2 = 100
(10)
2 = 100
100 = 100
Question 24 1 / -0
Which of the following equations can be obtained after completing the square of x2 + 4x - 1 = 0?
Solution
x2 + 4x - 1 = 0 (x +2)2 - 1 - 4 = 0 (x + 2)2 = 5
Question 25 1 / -0
If the quadratic equation ax2 + bx + c = 0 has no real roots, then ______.
Question 26 1 / -0
What will be the discriminant of the given quadratic equation? x2 + 7x - 1 = 0
Solution
x2 + 7x - 1 = 0 D = 49 - 4 (1) (- 1) = 53
Question 27 1 / -0
Which of the following equations can be obtained after completing the square of x2 - 10x + 5 = 0?
Solution
x2 - 10x + 5 = 0 (x - 5)2 + 5 - 25 = 0 (x - 5)2 = 20
Question 28 1 / -0
Which of the following equations has real and distinct roots?
Solution
5x2 - 11x - 12 = 0 D = 121 - 4 (5) (- 12) = 121 + 240 = 361 > 0 Hence real and distinct roots
Question 29 1 / -0
Which of the following equations has -1 as one of its solutions?
Solution
(x + 5)2 = 10 x = - 1 satisfy this (- 1 + 5)2 = 42 = 16
Question 30 1 / -0
Which of the following equations can be obtained after completing the square of 3x2 + 4x - 1 = 0?
Solution
3x
2 + 4x - 1 = 0
x
2 +
x -
= 0
= 0
(3x + 2)
2 = 7
Question 31 1 / -0
Which of the following quadratic equations has 0 as discriminant?
Solution
x2 + 4x + 4 = 0 D = 16 - 4 x 4 = 16 - 16 = 0
Question 32 1 / -0
Which of the following equations has 8 as one of its solutions?
Solution
(2x - 5)2 = 121 x = 8 satisfies this (2 x 8 - 5)2 = (16 - 5)2 = 112 = 121
Question 33 1 / -0
Which of the following equations has no real roots?
Solution
7x2 - 3x + 5 = 0 D = 9 - 140 = - 131 hence no real roots.
Question 34 1 / -0
Which of the following equations can be obtained after completing the square of 3x2 - 11x - 4 = 0?
Solution
3x
2 - 11x - 4 = 0
x
2 -
x -
= 0
= 0
Question 35 1 / -0
Which of the following equations has 56 as discriminant?
Solution
(1) D = 16 - 56 = - 40 (2) D = 64 + 8 = 72 (3) = 64 - 8 = 56
Question 36 1 / -0
Which of the following equations has -
as one of its solutions?
Solution
-
as a solution?
(x - 2
)
2 = 18
(-
)
2 (- 3
)
2 9 x 2 = 18
Question 37 1 / -0
Which of the following equations has equal roots?
Solution
x2 + 4x + 4 = 0 D = 16 - 16 = 0 has equal roots.
Question 38 1 / -0
Which of the following equations can be obtained after completing the square of 2x2 - 3x + 1 = 0?
Solution
2x
2 - 3x + 1 = 0
x
2 -
= 0
= 0
Question 39 1 / -0
What will be the discriminant of the given quadratic equation? x2 + x + 1 = 2
Solution
x2 + x + 1 = 2 x2 + x - 1 = 0 D = 1 - 4 (- 1) = 5
Question 40 1 / -0
Which of the following equations can be obtained after completing the square of 3x2 + 7x + 2 = 0?
Solution
3x
2 + 7x + 2 = 0
x
2 +
= 0
= 0