Determine the nature of the roots of the following quadratic equations:

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

Given:

Given quadratic equation is $\frac{3}{5}x^2 - \frac{2}{3}x + 1 = 0$.

To do:

We have to determine the nature of the roots of the given quadratic equation.

Solution:

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=\frac{3}{5}, b=-\frac{2}{3}$ and $c=1$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

Therefore,

$D=(-\frac{2}{3})^2-4(\frac{3}{5})(1)=\frac{4}{9}-\frac{12}{5}$

$=\frac{4\times5-12\times9}{45}$

$=\frac{20-108}{45}$

$=\frac{-88}{45}<0$

As $D<0$, the given quadratic equation has no real roots.

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Updated on: 10-Oct-2022

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