Question
The following are quadratic equations in $x$?
$\text{x}+\frac{2}{\text{x}}=\text{x}^2$
$\text{x}+\frac{2}{\text{x}}=\text{x}^2$
✓
Answer
$\text{x}+\frac{2}{\text{x}}=\text{x}^2$
$\Rightarrow x^2 + 2 = x^3$
$\Rightarrow x^3 - x^2 - 2 = 0$
And $(x^3- x^2 - 2)$ Being a polynomial of degree $3$, it is a quadratic polynomial.
Hence $\text{x}+\frac{2}{\text{x}}=\text{x}^2$ is a quadratic equation.
$\Rightarrow x^2 + 2 = x^3$
$\Rightarrow x^3 - x^2 - 2 = 0$
And $(x^3- x^2 - 2)$ Being a polynomial of degree $3$, it is a quadratic polynomial.
Hence $\text{x}+\frac{2}{\text{x}}=\text{x}^2$ is a quadratic equation.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Solve the following quadratic equation:$\sqrt3\text{x}^2+\text{11x}+6\sqrt3=0$
→If one root of the quadratic equation $3 y^2-k y+8=0$ is $\frac{2}{3}$, then find the value of $k$.
→Very-Short and Short-Answer Questions:
The cost of 5 pens and 8 pencils is ₹ 120, while the cost of 8 pens and 5 pencils is ₹ 153. Find the cost of 1 pen and that of 1 pencil.
The cost of 5 pens and 8 pencils is ₹ 120, while the cost of 8 pens and 5 pencils is ₹ 153. Find the cost of 1 pen and that of 1 pencil.
A sector of a circle of radius 8cm contains an angle of 135°. Find the area of the sector.
What is the probability that a number selected at random from the numbers 3, 4, 5, .... 9 is a multiple of 4?
Define HCF of two positive integers and find the HCF of the following pairs of numbers:
32 and 54
32 and 54
The first term a and common difference d are given. Find first four terms of A.P :
→$a=200, d=7$
Show that the roots of the equation $x^2 + px - q^2 = 0$ are real for all real value of p and q.
→In the given figure, an equilateral triangle has been inscribed in a circle of radius 4cm. Find the area of the shaded region. $\big[\text{Take }\pi=3.14\text{ and }\sqrt{3}=1.73.\big]$
→solve :$4 m+3 n=18 ; 3 m-2 n=5$
→