CBSE Questions for Class 10 Maths Quadratic Equations Quiz 3 - MCQExams.com

Solution of the equation   $$2x^{2} = 4x + 3$$   is
  • $$\dfrac {2\pm \sqrt {10}}{2}$$
  • $$\dfrac {2\pm 5\sqrt {2}}{2}$$
  • $$1\pm \sqrt {5}$$
  • $$1\pm \sqrt {10}$$
The discrimination of $$ax^{2} - (a + b)x + b = 0$$ is
  • $$a - b$$
  • $$a + b$$
  • $$(a + b)^{2}$$
  • $$(a - b)^{2}$$
Which of the following is a quadratic equation?
  • $$x^{1/2} + 2x + 3 = 0$$
  • $$(x - 1)(x + 4) = x^{2} + 1$$
  • $$x^{2} - 3x + 5 = 0$$
  • $$(2x + 1)(3x - 4) = 6x^{2} + 3$$
Solve the given equation by the method of Completion of Squares: $${x}^{2}+4x+4=0$$?
  • $$2$$
  • $$-2$$
  • $$4$$
  • $$-4$$
The discriminant ($$D$$) of the equation $$5x-6+\cfrac { 1 }{ x } =0$$ is ............
  • $$4$$
  • $$\sqrt { 56 } $$
  • $$16$$
  • $$56$$
The roots of quadratic equation $$\dfrac{x}{k} = \dfrac{k}{x} $$ are ...........
  • $$k, -k$$
  • $$-k, -k$$
  • $$k, k$$
  • $$k^2, - k^2$$
 The following equation is a quadratic equation.
 $$(x \, + \, 2)^3 \, = \, x^3 \, - \, 4$$
  • True
  • False
__________ is true for the discriminant of a quadratic equation $$x^2+x+1=0$$.
  • $$D=0$$
  • $$D<0$$
  • $$D>0$$
  • $$D$$ is a perfect square
The number of triples $$(x, y, z)$$ of real numbers satisfying the equation
$$x^{4} + y^{4} + z^{4} + 1 = 4xyz$$ is
  • $$0$$
  • $$4$$
  • $$8$$
  • More than $$8$$
The following equation is a qudratic equation.
 $$16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$$
  • True
  • False
Check whether the given equation is a quadratic equation or not.
$$2{ x }^{ 2 }-7x=0\quad $$
  • True
  • False
Which of the following methods is/are guaranteed to solve any Quadratic Equation?
  • Factorisation Method
  • Completing Square Method
  • Standard Quadratic Formula
  • Both option b and option c
Identify which of the following equations is a Quadratic Equation.
  • $$5x + 8 = 0$$
  • $$-2x^2+x=21$$
  • $$ax + by + c = 0$$
  • None of these.

The Completing Square Method converts the quadratic equation $$ax^2+bx+c=0$$ into which of the following forms?
  • $$(px+q)(rx+s)=0$$
  • $$px+q=0$$
  • $$(x+p)^2=q$$
  • All of the above.

For a quadratic equation in the standard form $$ax^2+bx+c=0$$, the nature of roots is dependent on the value of ?
  • $$b^2+4ac$$
  • $$b^2 \pm 4ac$$
  • $$\sqrt{b^2}-4ac$$
  • $$b^2-4ac$$
Check whether the given equation is a quadratic equation or not.
$${ x }^{ 2 }+2\sqrt { x } -3$$
  • True
  • False
The discriminant of the quadratic equation $${ x }^{ 2 }-4x+a=0$$ is $$16-4a$$.
  • True
  • False
Which of the following is a Quadratic Equation?
  • $$5x + 8 = 0$$
  • $$6x^2 + 7x =19$$
  • $$ x + 1$$
  • None of these
Assertion (A): The equation $$x-\displaystyle \cfrac{2}{x-1}=1-\cfrac{2}{x-1}$$ has no root.
Reason (R): $$x-1\neq 0$$, then only above equation is defined.
  • Both A and R are true and R is the correct explanation of A.
  • Both A and R are true and R is not the correct explanation of A.
  • A is true but R is false.
  • A is false but R is true
Find roots of equation $$x^2-11x+28=0$$ by quadratic formula 
  • $$4,7$$
  • $$-4,-7$$
  • $$4,-7$$
  • $$-4,7$$
If the roots of a quadratic equation $$ax^2+bx+c=0$$ are all real then which one of the following is true?
  • $$b^2-4ac=0$$
  • $$b^2-4ac>0$$
  • $$b^2-4ac\ge 0$$
  • $$b^2-4ac<0$$
If $$px^2 +qx+r=0$$ has equal roots, then $$q^2 =$$
  • $$4p$$
  • $$4pr$$
  • $$8pr$$
  • $$pr$$
If the roots of the equation $$ax^2+bx+c=0$$ are all real equal then which one of the following is true?
  • $$b^2-4ac=0$$
  • $$b^2-4ac\ge0$$
  • $$b^2-4ac<0$$
  • $$b^2-4ac>0$$
If the roots of a quadratic equation are equal, than discriminate is
  • $$1$$
  • $$0$$
  • greater than $$0$$
  • less than $$0$$
Which is a quadratic equation?
  • $$x+\dfrac{1}{x}=2$$
  • $$x^{2}+1=(x+3)^{2}$$
  • $$x(x+2)$$
  • $$x+\dfrac{1}{x}$$
The number of integral values of $$'x'$$ for which $$x^{2}+19x+92$$ is a perfect square is: 
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
The solution of the equation $$x+\cfrac{1}{x}=2$$ will be
  • $$2,-1$$
  • $$0,-1,-\cfrac{1}{5}$$
  • $$-1,-\cfrac{1}{5}$$
  • None of these
If $$81$$ is discriminant of $$2{ x }^{ 2 }+5x-k=0$$ then the value of $$k$$ is
  • $$5$$
  • $$7$$
  • $$-7$$
  • $$2$$
The value of $$\left( \frac { x - 3 } { x ^ { 2 } - x - 6 } + \frac { 2 x - 1 } { 2 x ^ { 2 } + 5 x - 3 } - \frac { 2 x + 5 } { x ^ { 2 } + 5 x + 6 } \right)$$ is:
  • $$\frac { x - 3 } { x - 2 }$$
  • $$- 1$$
  • $$1$$
  • $$0$$
Use the quadratic formula to solve $$x^2-4x-8=0$$.
  • $$2 \pm 2\sqrt 3$$
  • $$1 \pm \sqrt 3$$
  • $$3-3\sqrt 3$$
  • None of these
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