Question

EXERCISE 3A
1. Which of the following are quadratic equations
(1) x2 - x + 3=0
(2) 2x2 +1/5x-√3=0
(3) √2x2+7x+5√2=0.
(4) 1/3x2+1/5x-3=0
(5) x2-3x-√x+4=0
(6) x- 6/x=5
(7)x+2/x=x2
(8)x2 -1/x2=5​

Answer 1

(1) $x^{2}-x+3=0$

   Yes it is a quadratic equation because it is of the form $ax^{2}+bx+c=0$.

(2) $2x^{2}+\frac{1}{5x}-\sqrt{3} = 0$

     The given equation can be written as $10x^{3}-5\sqrt{3}x+1 =0$, this is not of the form $ax^{2}+bx+c=0$, so it is not a quadratic equation.

(3) $\sqrt{2}x^{2}+7x+5\sqrt{2}=0$

    Yes it is a quadratic equation because it is of the form $ax^{2}+bx+c=0$.

(4) $\frac{1}{3}x^{2} +\frac{1}{5x}-3=0$

     The given equation can be written as $5x^{3}-45x+3 =0$, this is not of the form $ax^{2}+bx+c=0$, so it is not a quadratic equation.

(5) $x^{2}-3x-\sqrt{x} +4=0$

    No it is not a quadratic equation because it is not of the form $ax^{2}+bx+c=0$.

(6) $x-\frac{6}{x}=5$

   The given equation can be written as $x^{2}-5x-6=0$, this is of the form $ax^{2}+bx+c=0$, so it is a quadratic equation.

(7) $x+\frac{2}{x}=x^{2}$

  The given equation can be written as $x^{3}- x^{2}-2=0$, this is not of the form $ax^{2}+bx+c=0$, so it is not a quadratic equation.

(8) $x^{2} -\frac{1}{x^{2} } =5$

   The given equation can be written as $x^{4}-5 x^{2} -1=0$, this is not of the form $ax^{2}+bx+c=0$, so it is not a quadratic equation.