QUADRATIC EQUATIONS Test

QUADRATIC EQUATIONS

This is QUADRATIC EQUATIONS Test-04 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
\({({x^2} + 1)^2} - {x^2} = 0\) has
  • A
    2 real roots
  • B
    1 real root
  • C
    no real roots
    Correct
  • D
    4 real roots
2
Which of the following has no real root?
  • A
    \({x^2} - 5x + 3\sqrt 2 = 0\)
  • B
    \({x^2} - 4x + 3\sqrt 2 = 0\)
    Correct
  • C
    \({x^2} - 4x - 3\sqrt 2 = 0\)
  • D
    \({x^2} + 4x - 3\sqrt 2 = 0\)
3
Which of the following has two distinct roots?
  • A
    \({x^2} + x - 5 = 0\)
    Correct
  • B
    \({x^2} + x + 5 = 0\)
  • C
    none of these
  • D
    \(5{x^2} - 3x + 1 = 0\)
4
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ is
  • A
    5
  • B
    6
    Correct
  • C
    3
  • D
    4
5
The discriminant of the quadratic equation \({\text{3}}\sqrt {\text{3}} {x^2} + 10x + \sqrt 3 = 0\) is
  • A
    72
  • B
    60
  • C
    64
    Correct
  • D
    62
6
The nature of the roots of the equation \(\sqrt {\text{3}} {x^2} - 2\sqrt 2 x - 2\sqrt 3 = 0\) is
  • A
    real and unequal
    Correct
  • B
    none of these
  • C
    not real
  • D
    real and equal
7
The quadratic equation whose roots are \(\frac{{{\text{ - 1}}}}{{\text{3}}}{\text{ and }}\frac{{\text{5}}}{{\text{2}}}{\text{ }}\) is
  • A
    \(6{x^2} + 13x + 5 = 0\)
  • B
    \(6{x^2} - 13x - 5 = 0\)
    Correct
  • C
    \(6{x^2} - 13x + 5 = 0\)
  • D
    \(6{x^2} + 13x - 5 = 0\)
8
The sum of the roots of the quadratic equation \(6{x^2} - 13x - 5 = 0\) is
  • A
    \(\frac{5}{6}\)
  • B
    \(\frac{{ - 5}}{6}\)
  • C
    \(\frac{{ - 13}}{6}\)
  • D
    \(\frac{{13}}{6}\)
    Correct
9
The product of the roots of the quadratic equation \(6{x^2} - 7x + 2 = 0\) is
  • A
    \(\frac{{ - 1}}{3}\)
  • B
    \(\frac{7}{6}\)
  • C
    \(\frac{{ - 7}}{6}\)
  • D
    \(\frac{1}{3}\)
    Correct
10
The smallest value of ‘k’ for which the quadratic equation \({x^2} + kx + 9 = 0\) has real roots is
  • A
    36
  • B
    – 3
  • C
    6
  • D
    – 6
    Correct
11
For what value of ‘p’, the quadratic equation \({x^2}--{\text{ }}4x{\text{ }} + {\text{ }}p{\text{ }} = {\text{ }}0\) has real roots?
  • A
    p = 4
  • B
    p=-4
  • C
    \(\begin{array}{*{20}{l}} {p{\text{ }} \leqslant {\text{ }}4} \end{array}\)
    Correct
  • D
    \(\begin{array}{*{20}{l}} {p{\text{ }} \geqslant {\text{ }}4} \end{array}\)
12
If the equation \(({a^2} + {b^2}){x^2} - 2(ac + bd)x + {c^2} + {d^2} = 0\) has equal roots, then
  • A
    \(ad = bc\)
    Correct
  • B
    \(ad = \sqrt {bc} \)
  • C
    \(ab = cd\)
  • D
    \(ab = \sqrt {cd} \)
13
If the roots of the equation \(({a^2} + {b^2}){x^2} - 2b(a + c)x + {c^2} + {b^2} = 0\) are equal, then
  • A
    \({b^2} = ac\)
    Correct
  • B
    \(b = \frac{{2ac}}{{a + c}}\)
  • C
    \(b = ac\)
  • D
    \(2b = a + c\)
14
If the sum of the roots of \({x^2} - x = \lambda (2x - 1)\) is zero, then the value of ‘\(\lambda \)’ is
  • A
    \(\frac{1}{2}\)
  • B
    – 2
  • C
    \(\frac{{ - 1}}{2}\)
    Correct
  • D
    2
15
The ratio of sum and the product of the roots of \(7{x^2} - 12x + 18 = 0\) is
  • A
    \(7:18\)
  • B
    \(7:12\)
  • C
    \(3:2\)
  • D
    \(2:3\)
    Correct