Quadratic Equations Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
21). If one roots of the equation is reciprocal of the other, then which one of the following is correct?
A). a = b
B). b = c
C). ac = 1
D). a = c
22). Number of solutions of the equation \( \Large \sqrt{x^{2}-x+1}+\frac{1}{\sqrt{x^{2}-x+1}}=2-x^{2} \) is
A). 0
B). 1
C). 2
D). 4
23). If \( \Large x = \sqrt{\frac{\sqrt{5}+1}{\sqrt{5}-1}} \), then \( \Large x^{2}-x-1 \) is equal to
A). 0
B). 1
C). 2
D). 5
24). If one of the roots of the equation \( \Large x^{2}-bx+c=0 \) is the square of the other, then which of the following option is correct?
A). \( \Large b^{2} = 3bc+c^{2}+c \)
B). \( \Large c^{3} = 3bc+b^{2}+b \)
C). \( \Large 3bc = c^{3}+b^{2}+b \)
D). \( \Large 3bc = c^{3}+b^{3}+b^{2} \)
25). Two students A and B solve an equation of the form \( \Large x^{2}+px+q=0 \). A starts with a wrong value of p and obtains the roots as 2 and 6. B starts with a wrong value of q and gets the roots as 2 and -9. What are the correct roots of the equation?
A). 3 and -4
B). -3 and -4
C). -3 and 4
D). 3 and 4


26). If the roots of equations \( \Large ax^{2}+bx+c=0 \) be \( \Large \ \alpha \  and\ \beta \) then the roots of equations \( \Large cx^{2}+bx+a=0 \) are:
A). \( \Large - \alpha ,\ - \beta \)
B). \( \Large \alpha ,\ \frac{1}{ \beta } \)
C). \( \Large \frac{1}{ \alpha },\ \frac{1}{ \beta } \)
D). none of these
27). Both the roots of the given equation. \( \Large \left(x-a\right) \left(x-b\right)+ \left(x-b\right) \left(x-c\right)+ \left(x-c\right) \left(x-a\right)=0 \) are always
A). positive
B). negative
C). real
D). imaginary
28). If the difference of roots of the equation \( \Large x^{2}-bx+c=0 \) be 1, then;
A). \( \Large b^{2}-4c-1=0 \)
B). \( \Large b^{2}-4c=0 \)
C). \( \Large b^{2}-4c+1=0 \)
D). \( \Large b^{2}+4c-1=0 \)
29). If \( \Large 2+i\sqrt{3} \) is a root of the equation \( \Large x^{2}+px+q=0 \) where p and q are real, then \( \Large p, q \) is equal to:
A). (-4, 7)
B). (4,-7)
C). (4, 7)
D). (-4, -7)
30). If \( \Large x=\sqrt{1+\sqrt{1+\sqrt{1}+.....}} \), the x is equal to
A). \( \Large \frac{1+\sqrt{5}}{2} \)
B). \( \Large \frac{1-\sqrt{5}}{2} \)
C). \( \Large \frac{1\pm \sqrt{5}}{2} \)
D). none of these .
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