CBSE Questions for Class 10 Maths Quadratic Equations Quiz 8 - MCQExams.com

Find the roots of the equation by the method of Completion of Squares:
$$x^2 - 6x + 9 = 0$$
  • $$3, 3$$
  • $$-3, -3$$
  • $$2, 2$$
  • $$-1, -1$$
If the roots of the quadratic equation $$5x^{2} - 2kx + 20 = 0$$ are real and equal then the value of $$k$$ is ________.
  • $$20$$
  • $$-10$$
  • $$10$$ or $$-10$$
  • $$10$$
Find the roots of the quadratic equation $$x^2+2x+3=0$$.
  • 0,1
  • $$-1-$$ $$\sqrt2$$$$i$$ , $$-1+\sqrt2$$$$i$$
  • $$1+i,1-i$$
  • None
Given the roots of $$x^2 - px + 8p - 15 = 0$$ are equal, the value of p is equal to
  • $$3 , 5$$
  • $$2 , 5$$
  • $$3 , 6$$
  • $$2 ,30$$
Find the roots of the following quadratic equation (if they exist) by the method of completing the square.
$$x^2 \, - \, (\sqrt{2} \, + \, 1)  \, x \, + \, \sqrt{2} \, = \, 0$$
  • $$exist, \sqrt2$$, $$1$$
  • $$exist, -\sqrt2$$, $$1$$
  • $$exist, -\sqrt2$$, $$-1$$
  • $$\text{does not exist}$$
State true or false:
The roots of the quadratic equation $$2x^2 + x - 4 = 0$$  are $$\dfrac{-1+\sqrt{33} }{4}$$ and $$ \dfrac{-1-\sqrt{33} }{4}$$ (if they exist).
  • True
  • False
In the following, determine whether the given values are solutions of the given equation or not :
 $$x^2 \, - \, 3\sqrt{3x} \, + \, 6 \, = \, 0, \, x \, = \, \sqrt{3}, \, x \, = \, -2\sqrt{3}$$
  • $$x = \sqrt3$$ is not a solution but $$x = -2\sqrt3$$ is a solution.
  • $$x = \sqrt3$$ is a solution but $$x = -2\sqrt3$$ is not a solution.
  • $$x = \sqrt3$$ and $$x = -2\sqrt3$$ are not solutions.
  • $$x = \sqrt3$$ and $$x = -2\sqrt3$$ are solutions.
The roots of the following quadratic equation (if they exist) by the method of completing the square.
$$x^2 \, - \, 4\sqrt{2x} \, + \, 6 \, = \, 0$$
are$$\sqrt2, \, 3\sqrt2$$
  • True
  • False
The roots of the following quadratic equation (if they exist) by the method of completing the square.
$$4x^2 \, + \, 4\sqrt{3}x \, + \, 3 \, = \, 0$$
are $$\dfrac{-\sqrt3}{2}, \, \dfrac{-\sqrt3}{2}$$
  • True
  • False
The roots of the quadratic equation $$\sqrt{2}x^2 - 3x - 2\sqrt{2} = 0$$ (if they exist) by the method of completing the square are $$-\dfrac1{\sqrt2},\ 2\sqrt2.$$
  • True
  • False
The roots of the quadratic equation $$3x^2 + 11x + 10 = 0$$ (if they exist) by the method of completing the square are $$-\dfrac{5}{3},\ -2.$$
  • True
  • False
The roots of the following quadratic equation (if they exist) by the method of completing the square.
$$2x^2  - 7x + 3 = 0$$ are $$3$$, $$\dfrac{1}{2}$$
  • True
  • False
The equation $$a^2$$ - 2a sinx + 1 has only two possible real solutions for a .
  • True
  • False

Which of the following statements is TRUE/CORRECT about Quadratic Equations? A quadratic equation is _____
  • An expression with a single variable and degree $$2$$.
  • An equation with a single variable and degree $$2$$.
  • An equation with degree $$2$$ only.
  • An equation with single variable only.
Check whether the given equation is a quadratic equation or not.
$$\quad { x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } } =2\quad $$
  • True
  • False
Check whether the given equation is a quadratic equation or not.
$$3{ x }^{ 2 }-4x+2=2{ x }^{ 2 }-2x+4$$
  • True
  • False
Solve by the method of completing the square $$5x^2 - 6x - 2 = 0$$
  • $$\frac{3+\sqrt{19}}{5}$$ $$and$$ $$\frac{3-\sqrt{19}}{5}$$ 
  • $$\frac{-3+\sqrt{19}}{5}$$ $$and$$ $$\frac{3-\sqrt{19}}{5}$$ 
  • $$\frac{3+\sqrt{19}}{3}$$ $$and$$ $$\frac{3-\sqrt{19}}{5}$$ 
  • $$\frac{3+\sqrt{19}}{5}$$ $$and$$ $$\frac{-3-\sqrt{19}}{3}$$ 
Solve:
$$x^{2}-2x+360=0$$
  • $$x=1\pm\sqrt{-359}$$
  • $$x=2\pm\sqrt{-359}$$
  • $$x=1\pm\sqrt{359}$$
  • None of these
Roots of the equation $$2{x}^{2}-5x+1=0$$, $${x}^{2}+5x+2=0$$ are
  • reciprocal and of same sign
  • reciprocal and of opposite sign
  • equal in product
  • None of these
Two water taps together can fill a tank in $$3\dfrac {1}{13}$$ hours. The tap of longer diameter takes $$3$$ hours less then smaller one to fill the bank separately. Find the time(hrs) in which tap of smaller diameter can separately fill the tank.
  • $$5$$
  • $$3$$
  • $$8$$
  • None of these
Find the roots of the equation $$5x^{2} -6x-2 = 0$$ by the method of completing the square.
  • $$\dfrac{3\pm\sqrt{76}}{2}$$
  • $$\dfrac{3\pm\sqrt{19}}{4}$$
  • $$\dfrac{3\pm\sqrt{76}}{10}$$
  • $$\dfrac{3\pm\sqrt{19}}{5}$$
The value of $$'a'$$ for which the quadratic equation $$2{x^2} - x\left( {{a^2} + 8a - 1} \right) + {a^2} - 4a = 0$$ has roots opposite signs, lie in the interval 
  • $$1 < a < 5$$
  • $$0 < a < 4$$
  • $$ - 1 < a < 2$$
  • $$2 < a < 6$$
The equation $$10x -\dfrac{1}{x} = 3$$ when solved by the method of completing the square yields x $$=$$ 0.5.
  • True
  • False
The roots of the given equation $$\left( {p - q} \right){x^2} + \left( {q - r} \right)x + \left( {r - p} \right) = 0$$  are 
  • $$\dfrac{{p - q}}{{r - p}},1$$
  • $$\dfrac{{q - r}}{{p - q}},1$$
  • $$\dfrac{{r - p}}{{p - q}},1$$
  • $$1,\dfrac{{q - r}}{{p - q}}$$
If $$\alpha $$ and $$\beta $$ are the roots of equation $${x^2} - 3x + 1 = 0$$ and $${a_n} = {\alpha ^n} + {\beta ^n},n \in N$$ then the value of $$\dfrac{{{a_7} + {a_5}}}{{{a_6}}}$$
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The sum of the roots of the quadratic $$5x^{2}-6x+1=0$$ is
  • $$-\dfrac{6}{5}$$
  • $$\dfrac{1}{5}$$
  • $$-\dfrac{5}{6}$$
  • $$-\dfrac{1}{5}$$
If $$\alpha,\beta$$ are the roots of $${x}^{2}-x+1=0$$ then $$\cfrac { { \left( { \alpha  }^{ 2 }-\alpha  \right)  }^{ 3 }+{ \left( { \beta  }^{ 2 }-\beta  \right)  }^{ 3 } }{ \left( 2-\alpha  \right) \left( 2-\beta  \right)  } $$ is equal to
  • $$0$$
  • $$1$$
  • $$\dfrac{-2}{3}$$
  • $$2$$
The roots of  $$a{x^2} + bx + c = 0$$ where $$a \ne 0$$ and coefficients are real and $$a+c <b$$, then
  • $$4a+c>2b$$
  • $$4a+c<2b$$
  • $$4a+c=2b$$
  • none of the above
If $$p, q, r$$ are the roots of the cubic equation $$x^3-3x+4=0$$, then value of $$\dfrac{1}{p^3+q^3+8}+\dfrac{1}{q^3+r^3+8}+\dfrac{1}{r^3+p^3+8}$$ is equal to
  • maximum value of $$f(x)=-x^2+2x-\frac{1}{4}\forall x\in \begin{bmatrix}
    -2,2
    \end{bmatrix}$$
  • minimum value of $$g(x)=2x^2-3x+\frac{7}{8}\forall x\in \begin{bmatrix}
    -1,1
    \end{bmatrix}$$
  • $$-\frac{1}{\alpha }$$ where $$\alpha $$ is characteristic of $$\log_9(6569)$$
  • value of $$\log_{(antilog_{128}\left(\frac{4}{7}\right)}\left(\dfrac {1}{2}\right)$$
In the quadratic equation $$x^2+(p+iq)x+3i=0$$, $$p$$ and $$q$$ are real. If the sum of the square of the squares of the roots is $$8$$ then find the values of $$p$$ & $$ \ q$$ 
  • $$p=3,q=-1$$
  • $$p=-3,q=-1$$
  • $$p=3,q=1$$ or $$p=-3,q=-1$$
  • $$p=-3,q=1$$
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