Quadratic Equations Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
51). If x is real the expression \( \Large \frac{x+2}{2x^{2}+3x+6} \) takes all values in the interval:
A). \( \Large \left(\frac{1}{13}, \frac{1}{3}\right) \)
B). \( \Large \left(- \frac{1}{13}, \frac{1}{3}\right) \)
C). \( \Large \left(- \frac{1}{3}, \frac{1}{13}\right) \)
D). none of these.
52). If x is real, then the maximum and minimum values of the expression \( \Large \frac{x^{2}
-3x+4}{x^{2}+3x+4} \) will be:

A). 2,1
B). \( \Large 5, \frac{1}{5} \)
C). \( \Large 7, \frac{1}{7} \)
D). none of these.
53). The number of real solutions of the equation \( \Large |x^{2}+4x+3|+2x+5=0 \) are:
A). 1
B). 2
C). 3
D). 4
54). If the roots of the given equation:
\( \Large \left(\cos p-1\right)x^{2}+ \left(\cos p\right)x+\sin p = 0 \) are real, then:

A). \( \Large P \epsilon \left(- \pi ,0\right) \)
B). \( \Large P \epsilon \left(- \frac{ \pi }{2}, \frac{ \pi }{2} \right) \)
C). \( \Large P \epsilon \left(0, \pi \right) \)
D). \( \Large P \epsilon \left(0, 2 \pi \right) \)
55). The solution of the quadratic equation \( \Large \left(3|x|-3\right)^{2}=|x|+7 \) which belongs to the domain of definition of function \( \Large \gamma = \sqrt{x \left(x-3\right) } \) are given by:
A). \( \Large \pm \frac{1}{9}, \pm 2 \)
B). \( \Large -\frac{1}{9}, 2 \)
C). \( \Large \frac{1}{9}, -2 \)
D). \( \Large -\frac{1}{9}, -2 \)


56). The number of solution of \( \Large \frac{log 5 + log \left(x^{2}+1\right) }{log \left(x-2\right) }=2 \)
A). 2
B). 3
C). 1
D). none of these
57). If the expression \( \Large \left(mx-1+\frac{1}{x}\right) \) is always nonnegative, then the minimum value of m must be:
A). \( \Large -\frac{1}{2} \)
B). 0
C). \( \Large \frac{1}{4} \)
D). \( \Large \frac{1}{2} \)
58). The value of x in the given equation \( \Large 4^{x}-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1} \) is:
A). \( \Large \frac{4}{3} \)
B). \( \Large \frac{3}{2} \)
C). \( \Large \frac{2}{1} \)
D). \( \Large \frac{5}{3} \)
59). The harmonic mean of the roots of equation \( \Large \left(5+\sqrt{2}x^{2}-14+\sqrt{5}\right)x+8+2\sqrt{5}=0 \) is:
A). 2
B). 4
C). 6
D). 8
60). For what value of \( \Large \lambda \) the sum of the squares of the roots of \( \Large x^{2}+ \left(2+\lambda\right)n-\frac{1}{2} \left(1+\lambda\right)=0 \) is minimum?
A). \( \Large \frac{3}{2} \)
B). 1
C). \( \Large \frac{1}{2} \)
D). \( \Large \frac{11}{4} \)
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