Olympiad – Class X – Mathematics - Quadratic Equations

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Question - 1

Identify the quadratic equation from the following.

  • A \(p+\frac { 1 }{ p } =1,p\neq 0\)
  • B \(p^{ 2 }+\frac { 1 }{ p } =1,p\neq 0\)
  • C x2-\(\frac { 1 }{ x } =1,x\neq 0\)
  • D x2+2\(\sqrt { x } \)-1=0

Question - 2

Find the roots of the quadratic equation 2m2 + 3m + 1 = 0

  • A \(\frac { -1 }{ 2 } \),1
  • B -1,\(\frac { 1 }{ 2 } \)
  • C \(\frac { 1 }{ 2 } \),1
  • D -1,\(\frac { -1 }{ 2 } \)

Question - 3

Which of the following statements is correct?

  • A x = 1 is a root of 2x2+ 3x + 1 =0
  • B x = 2 is not a root of 6x2 + 7x - 5 = 0
  • C x = -1 is a root of 3x2 -x -1 = 0
  • D x =\(-\frac { 2 }{ 5 } \)is not a root 5x2-8x-4 = O

Question - 4

Find the value of 'p' for which m = \(\frac { 1 }{ \sqrt { 3 } } \) is a root of the equation pm2+(\(\sqrt { 3 } -\sqrt { 2 } \))m-1=0

  • A \(\sqrt { 3 } \)
  • B \(\sqrt { 2 } \)
  • C \(\sqrt { 6} \)
  • D \(\sqrt { 7} \)

Question - 5

For what respective values of 'm' and 'n' are x =\(\frac { -2 }{ 5 } \) and x=\(\frac { 5 }{ 3 } \) the roots of rnx2- + nx - 10 = 0?

  • A 15,-19
  • B -19,15
  • C 19,-15
  • D -15,19

Question - 6

The sides of two square plots are (2x - 1) m and (5x + 4) m. The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot

  • A 15 m
  • B 13 m
  • C 31 m
  • D 39 m

Question - 7

What are the roots of 17a2- 20a + 10 = 10a2+ 2a + 7

  • A \(\frac { 1 }{ 7 } \),3
  • B 3,\(\frac { -1 }{ 7 } \)
  • C \(\frac { -1 }{ 7 } \),-3
  • D -3,\(-\frac { 1 }{ 7 } \)

Question - 8

Identify the factors of \(\frac { { 4x }^{ 2 } }{ 5 } \)=4x-5

  • A \(\frac { 2 }{ 5 } ,\frac { 2 }{ 5 } \)
  • B \(\frac { -5 }{ 2 } ,\frac { 5 }{ 2 } \)
  • C \(\frac { 5 }{ 2 } ,\frac { 5 }{ 2 } \)
  • D \(\frac { -2 }{ 5 } ,\frac { 2 }{ 5 } \)

Question - 9

The age of a man is the square of his son's age. A year ago, the man's age was eight times the age of his son. What is the present age of the man?

  • A 47 years
  • B 49 years
  • C 36 years
  • D 48 years

Question - 10

Find two consecutive even numbers whose product is double that of the greater number.

  • A 1,3
  • B 4,6
  • C 2,4
  • D 6,8
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