Check whether the following are quadratic equations:2x^2-3\sqrt{x}

Class 10

Math

All topics

Complex Number and Quadratic Equations

577

150

Check whether the following are quadratic equations:
$2 x^{2} - 3 x + 5 = 0$

Solution:

Given,

2 x^{2} - 3 x + 5 = 0

\Rightarrow 2 x^{2} + 5 = 3 x

\Rightarrow (2 x^{2} + 5)^{2} = (3 x)^{2}

\Rightarrow 4 x^{4} + 20 x^{2} + 25 = 9 x

\Rightarrow 4 x^{2} + 20 x^{2} - 9 x + 25 = 0

∵

The highest power of x in the equation is 4;

∴

It is not a quadratic equation.

577

150

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Related Questions

If the multiplicative inverse of a complex number is $\frac{3 + 4 i}{19}$ where $i = - 1$ , then find complex number.

If $z_{1}, z_{2}$ are complex numbers such that Re $(z_{1}) = ∣ z_{1} - 2 ∣, R e (z_{2}) = ∣ z_{2} - 2 ∣$ and $A r g (z_{1} - z_{2}) = π /3$ , then $I m (z_{1} + z_{2}) =$

Show that

\frac{7 + i 3}{7 - i 3} + \frac{7 - i 3}{7 + i 3}

is real.

If $(1 + i 3)^{1999} = a + ib,$ then

Find real $θ$ such that $\frac{1 + i cos θ}{1 - 2 i cos θ}$ is purely imaginary

If $z_{1} = \frac{1}{a + i}, a \neq = 0$ and $z_{2} = \frac{1}{1 + bi}, b \neq = 0$ are such that $z_{1} = \overset{z}{ˉ}_{2}$ then

$\frac{( 1 + i ) ^{2011}}{( 1 + i ) ^{2009}}$ =

If $8 i z^{3} + 12 z^{2} - 18 z + 27 i = 0$ , find $4∣ z ∣^{2}$ .