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
41). If one root of the equation \( \Large x^{2}+px+12=0 \) is 4, while the equation \( \Large x^{2}-7x+q=0 \) has equal roots, then the value of 'g' is:
A). \( \Large \frac{49}{4} \)
B). 12
C). 3
D). 4
42). Let \( \Large 2\sin^{2}+3\sin x-2>0 \) and \( \Large x^{2}-x-2<0 \) (x is measured in radians). Then x lies in the interval:
A). \( \Large \left(\frac{ \pi }{6},\frac{5 \pi }{6}\right) \)
B). \( \Large \left(-1, \frac{5 \pi }{6}\right) \)
C). \( \Large \left(-1, 2\right) \)
D). \( \Large \left(\frac{ \pi }{6}, 2\right) \)
43). If at least one root of \( \Large 2x^{2}+3x+5=0 \) and \( \Large ax^{2}+bx+c=0 \), a, b, c, belongs to N is common, then the maximum value of a + b + c is:
A). 10
B). 0
C). does not exist
D). none of these
44). If the roots of the quadratic equation \( \Large x^{2}+px+q=0 \) are \( \Large \tan 30 ^{\circ} and\ \tan 15 ^{\circ} \) respectively, then the value of\( \Large 2+q-p \) is
A). 3
B). 0
C). 1
D). 2
45). If \( \Large P \left(x\right)=ax^{2}+bx+c \) and \( \Large Q \left(x\right)=-ax^{2}+dx+c \) where \( \Large ac \ne 0 \) then \( \Large P \left(x\right) Q \left(x\right) = 0 \) has at least:
A). four real roots
B). two real roots
C). four imaginary roots
D). none of these


46). The coefficient of x in the equation \( \Large x^{2}+px+q=0 \) was taken as 17 in place of 13 its roots Were found to be -2 and -15. The roots of the original equation are:
A). 3,10
B). -3 , -10
C). -5, -8
D). None of these
47). The number which exceeds its positive Square roots by 12 is:
A). 9
B). 16
C). 25
D). none of these
48). Let a, b, c be real numbers a \( \ne \) 0. If \( \Large \alpha \) is a root of \( \Large a^{2}x^{2}+bx+c=0, \),\( \Large \beta \) is a root of \( \Large a^{2}x^{2}-bx-c=0 \) and \( \Large 0< \alpha < \beta \) then the equation \( \Large a^{2}x^{2}+2bx+2c=0 \) has a root of \( \gamma \) that always satisfies:
A). \( \Large \gamma = \frac{ \alpha + \beta }{2} \)
B). \( \Large \gamma = \alpha + \frac{ \beta }{2} \)
C). \( \Large \gamma = \alpha \)
D). \( \Large \alpha < \gamma < \beta \)
49). The equation \( \Large x \left(\frac{3}{4}log_{2}x\right)^{2}+ \left(log_{2}x\right)
-\frac{5}{4}=\sqrt{2} \) has

A). at least one real solution
B). exactly three real solution
C). exactly one irrational solution.
D). all of the above
50). The solution of set of the equation \( \Large x log x \left(1-x\right)^{2}=9 \) is
A). \( \Large \{ -2, 4 \} \)
B). \( \Large \{ 4 \} \)
C). \( \Large \{ 0, -2, 4 \} \)
D). none of these
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