Question

Find the roots of the quadratic equation 3x square+2x-1=0, by using the quadratic formula and the nature of the roots​

Answer 1

Answer:

The roots of the equation are: -1 and 1/3

Nature of roots: Real and Unequal.

Step-by-step explanation:

Given equation is

$3 {x}^{2} + 2x - 1$

Using quadratic formula

$x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} \\ = > \frac{ - 2 ± \sqrt{4 - 4(3)( - 1)} }{6} \\ = > \frac{ - 2± \sqrt{16} }{6} \\ = > \frac{ - 2 ± 4}{6} \\ = > - 1 \: or \frac{1}{3}$

Talking about the Nature of the roots, one way to check it is directly investigating the roots obtained above. We can clearly see that the roots are Real and Unequal.

The other way is to calculate the discriminant.

• If the discriminant is less than zero, the roots are Imaginary and Unequal.
• If the discriminant is greater than zero, the roots are Real and Unequal.
• If the discriminant is equal to zero, the roots are Real and Equal.

Here, in this case the discriminant is

$\sqrt{ {b}^{2} - 4(a)(c) } \\ = > \sqrt{4 - 4(3)( - 1)} \\ = > \sqrt{16} \\ = > 4$

which is greater than zero, So the roots are Real and Unequal.

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