Range of Quadratic Expression
Trending Questions
Q. 16. The equation {x²/(1-r)}-{y²/(1+r)}=1, r>1 represents 1. Ellipse 2. Hyperbola 3. Circle 4. None
Q.
Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations:
3x−y−z=0−3x+z=0−3x+2y+z=0
Then the number of such points for which
x2+y2+z2≤100 is
Q.
The number of real solutions of the equation x2+3|x|+2 =0 is:
0
1
2
4
Q. The range of f(x)=−x2+7x+60 in x∈[−3, 2] is
- [30, 70]
- [30, 2894]
- [70, 2894]
- [30, 2894)
Q. The largest natural number ′a′ for which the maximum value of f(x)=a−1+2x−x2 is always smaller than the minimum value of g(x)=x2−2ax+10−2a is
- 1
- 2
- 3
- 4
Q.
Let x3+ax+1=0 and x4+ax2+1=0 have a common root. Then a =
1
-1
2
-2
Q. If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to :
- 32
- 34
- 54
- 74
Q. The number of integral values of λ for which the equation x2 + y2 + λx + (1 − λ) y + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is
(a) 14
(b) 18
(c) 16
(d) none of these
(a) 14
(b) 18
(c) 16
(d) none of these
Q. For every possible x∈R, If x2+2x+ax2+4x+3a can take all real values, then
- a∈[0, 1]
- a∈(0, 1)
- a∈[−1, 1]
- a∈(−1, 1)
Q. The range of f(x)=xx2+4 is
- [−4, 4]
- [−12, 12]
- [−15, 15]
- [−14, 14]
Q. The maximum value of f(x)=x2+7x+9 is
- 9
- 134
- −134
- not defined
Q. For the ellipse 12x2 + 4y2 + 24x − 16y + 25 = 0
(a) centre is (−1, 2)
(b) lengths of the axes are and 1
(c) eccentricity =
(d) all of these
(a) centre is (−1, 2)
(b) lengths of the axes are and 1
(c) eccentricity =
(d) all of these
Q. The value of λ such that sum of the squares of the roots of the quadratic equation, x2+(3−λ)x+2=λ has the least value is:
- 49
- 2
- 1
- 158
Q. If f(x)=x2+2bx+2c2 and g(x)=−x2−2cx+b2 are such that the minimum value of f(x) always exceeds maximum value of g(x), then which of the following is/are correct?
- b=1, c=0
- b=2, c=3
- b=3, c=5
- b=4, c=5
Q. The focus of the parabola y = 2x2 + x is
(a) (0, 0)
(b) (1/2, 1/4)
(c) (−1/4, 0)
(d) (−1/4, 1/8)
(a) (0, 0)
(b) (1/2, 1/4)
(c) (−1/4, 0)
(d) (−1/4, 1/8)
Q. The maximum value of (12)x2−3x+2 is
(x∈R)
(x∈R)
- 14
- 4√2
- 0
- not defined
Q.
If the range of f(x) is (−(∞, ∞), then the range of g(x) = 1√f(x) is
(-
,
)
(0,
)
(-
, 0)
None of these
Q. The foci of the hyperbola 9x2 − 16y2 = 144 are
(a) (± 4, 0)
(b) (0, ± 4)
(c) (± 5, 0)
(d) (0, ± 5)
(a) (± 4, 0)
(b) (0, ± 4)
(c) (± 5, 0)
(d) (0, ± 5)
Q. The maximum value of the quadraticfunction y=−5x2+7x+2 is 710 .
- True
- False
Q. The range of f(x)=1−x2+4x+5, x∈R−{−1, 5} is
- (−∞, 0]∪[19, ∞)
- (−∞, 0)∪[19, ∞)
- (−∞, 0]∪(19, ∞)
- (−∞, 0)∪(19, ∞)
Q.
Which quadratic equation fits the data in the table?
Q. f:R→R, f(x)=3x2+mx+nx2+1. If the range of f(x) is [−4, 3], then
- m=0
- n=4
- m=2
- n=−4
Q. The number of real solutions of the equation x2−x+3+(910)x=0 is
- 2
- 0
- 1
- none of these
Q. Range of the rational expression y=x+32x2+3x+9, x∈R is
- [121, 13]
- [−121, 13]
- [−13, 13]
- [−121, 121]
Q. Number of positive integral value of 'p' for which the equation p.2ex+e−x−8.2ex+e−x2+p=0 has atleast one solution is
Q. If x is real, y=x2−3x+4x2+3x+4, then y will lie between .
- 17 and 7
- -1 and 1
- 15 and 5
- -3 and 3
Q. If the minimum value of f(x)=ax2+2x+5, a>0 is equal to the maximum value of g(x)=3+2x−x2, then the value of ′a′ is
- 3
- 1
- 2
- 4
Q. If the equation x2+9y2−4x+3=0 is satisfied for all real values of x and y, then
- x∈[1, 3]
- y∈[−13, 13]
- x∈(13, 3]
- y∈(−3, −13)
Q. Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).