Question
The following are quadratic equations in x?
$\text{x}-\frac{6}{\text{x}}=3$
$\text{x}-\frac{6}{\text{x}}=3$
✓
Answer
$\text{x}-\frac{6}{\text{x}}=3$
$\Rightarrow x^2- 6 = 3x$
$\Rightarrow x^2 - 3x - 6 = 0$
And $(x^2- 3x - 6)$ Being a polynomial of degree 2, it is a quadratic polynomial.
Hence $\text{x}-\frac{6}{\text{x}}=3$ is a quadratic equation.
$\Rightarrow x^2- 6 = 3x$
$\Rightarrow x^2 - 3x - 6 = 0$
And $(x^2- 3x - 6)$ Being a polynomial of degree 2, it is a quadratic polynomial.
Hence $\text{x}-\frac{6}{\text{x}}=3$ 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
A tower stands vertically on the ground. from a point on the ground which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^{\circ}$, find the height of the tower.
→Answer the following and justify:
Can the quadratic polynomial $x^2 + kx + k$ have equal zeroes for some odd integer $k > 1?$
→Can the quadratic polynomial $x^2 + kx + k$ have equal zeroes for some odd integer $k > 1?$
Very-Short and Short-Answer Questions:
Find the value of k for which the system 3x + 5y = 0 and kx + 10y = 0 has a nonzero solution.
Find the value of k for which the system 3x + 5y = 0 and kx + 10y = 0 has a nonzero solution.
What is the probability that an ordinary year has 53 Sundays?
In figure, find tan P - cot R.
Find the sum:
$25 + 28 + 31 + ..... + 100.$
→$25 + 28 + 31 + ..... + 100.$
If $f(x)=x^3+x^2-a x+b$ is divisible by $x^2-x$ write the value of $a$ and $b$.
→The $17^{\text {th }}$ term of $A P$ is 5 more than wich its $8^{\text {th }}$ term. If the $11^{\text {th }}$ term of the $A P$ is 43 , find its $n ^{\text {th }}$ term.
→In the figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10cm and CQ = 2cm, what is the length PC ?, if PB = 10cm, what is the perimeter of $\triangle\text{PCD}$?
→What is the maximum value of $\frac{1}{\text{cosec }\theta}?$
→