Question

which of the following equations are quadratic equations?x square-x=5x+4,2p+3 square/p=1,p+p cube=p square-1,m+1/m=2,1/y=2y+3,x cube=7x square-9,z+3=-2/z

Answer 1

Hey
x​2​​−x=5x+4 
x2−6x−4=0{x}^{2} - 6x - 4 = 0x​2​​−6x−4=0 

It is a quadratic equation..

2)
2p2+32p=12 {p}^{2} + \frac{ {3}^{2} }{p} = 12p​2​​+​p​​3​2​​​​=1 
2p2+9=p2 {p}^{2} + 9 = p2p​2​​+9=p 
2p2−p+9=02 {p}^{2} - p + 9 = 02p​2​​−p+9=0 
.It is a quadratic equation.

3) It is equation in cubical form so it is not a quadratic equation...

4)
m+1m=2\frac{m + 1}{m } = 2​m​​m+1​​=2 
m+1=2mm + 1 = 2mm+1=2m 

.. Hence it is not a quadratic equation....

5)
1y=2y+3\frac{1}{y} = 2y + 3​y​​1​​=2y+3 
2y2+3y=12 {y}^{2} + 3y = 12y​2​​+3y=1 
2y2+3y−1=02 {y}^{2} + 3y - 1 = 02y​2​​+3y−1=0 

It is a quadratic equation

6)
x3−7x2+9=0{x}^{3} - 7 {x}^{2} + 9 = 0x​3​​−7x​2​​+9=0 
It is equation in cubical form so it is not a quadratic equation...
..

7)
z+3=−3zz + 3 = \frac{ - 3}{z}z+3=​z​​−3​​ 
z2+3z+3=0{z}^{2} + 3z + 3 = 0z​2​​+3z+3=0 
It is a quadratic equation......

Answer 2

Hey friend quadratic equations are in the form
$a {x}^{2} + bx + c = 0$

1)
${x}^{2} - x = 5x + 4$
${x}^{2} - 6x - 4 = 0$

It is a quadratic equation..

2)
$2 {p}^{2} + \frac{ {3}^{2} }{p} = 1$
$2 {p}^{2} + 9 = p$
$2 {p}^{2} - p + 9 = 0$
.It is a quadratic equation.

3) It is equation in cubical form so it is not a quadratic equation...

4)
$\frac{m + 1}{m } = 2$
$m + 1 = 2m$

.. Hence it is not a quadratic equation....

5)
$\frac{1}{y} = 2y + 3$
$2 {y}^{2} + 3y = 1$
$2 {y}^{2} + 3y - 1 = 0$

It is a quadratic equation

6)
${x}^{3} - 7 {x}^{2} + 9 = 0$
It is equation in cubical form so it is not a quadratic equation...
..

7)
$z + 3 = \frac{ - 3}{z}$
${z}^{2} + 3z + 3 = 0$
It is a quadratic equation......