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
61). Given that \( \Large \tan \alpha \) and \( \Large \tan \beta \) are the roots of \( \Large x^{2}-px+q=0 \), then the value of \( \Large \sin^{2} \left(\alpha + \beta \right) \) is equal to:
A). \( \Large \frac{p^{2}}{p^{2}+ \left(1-q\right)^{2} } \)
B). \( \Large \frac{p^{2}}{p^{2}+q^{2}} \)
C). \( \Large \frac{q^{2}}{p^{2} \left(1-q\right)^{2} } \)
D). \( \Large \frac{p^{2}}{ \left(p+q\right)^{2} } \)
62). The number of values of K for which the system of equations \( \Large \left(K+1\right)x+84=4K \) and \( \Large Kx+ \left(K+3\right)y=3 K-1 \) has infinitely many solution, is:
A). 0
B). 1
C). 2
D). infinite
63). The set of all real numbers x for which \( \Large x^{2}-|x+2|+x>0 \) is:
A). \( \Large \left(-\infty, -2\right) \ \left(2, \infty\right) \)
B). \( \Large \left(-\infty, -\sqrt{2}\right) \ \left(\sqrt{2}, \infty\right) \)
C). \( \Large \left(-\infty, -1\right) \ \left(1, \infty\right) \)
D). \( \Large \left(\sqrt{2}, \infty\right) \)
64). Let a, b, c be positive numbers, the following systems of equations in x, y and z \( \Large \frac{x^{2}}{a^{2}} +\ \frac{y^{2}}{b^{2}}-\frac{z^{2}}{c^{2}}=1; \ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} +\ \frac{z^{2}}{c^{2}}=1 and\ \frac{-x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=1 \) has;
A). no solutions
B). unique solution
C). infinitely many solution
D). finitely many solution.
65). If \( \Large 2 \sin^{2}\frac{ \pi }{8} \) is a root of equation\( \Large x^{2}+ax+b=0 \), where a and b are rational numbers, then a - b is equal to
A). \( \Large -\frac{5}{2} \)
B). \( \Large -\frac{3}{2} \)
C). \( \Large -\frac{1}{2} \)
D). \( \Large \frac{1}{2} \)


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