Find the roots of the quadratic equations by using the quadratic formula in each of the following:
$ -3 x^{2}+5 x+12=0 $

Given:

Given quadratic equation is \( -3 x^{2}+5 x+12=0 \).

To do:

We have to find the roots of the given quadratic equation.

Solution:

$-3x^2+5x + 12 = 0$

The above equation is of the form $ax^2 + bx + c = 0$, where $a = -3, b = 5$ and $c =  12$

Discriminant $\mathrm{D} =b^{2}-4 a c$

$=(5)^{2}-4 \times (-3)\times12$

$=25+144$

$=169$

$\mathrm{D}>0$

Let the roots of the equation are $\alpha$ and $\beta$

$\alpha =\frac{-b+\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-5+\sqrt{169}}{2(-3)}$

$=\frac{-5+13}{-6}$

$=\frac{8}{-6}$

$=-\frac{4}{3}$

$\beta =\frac{-b-\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-5-\sqrt{169}}{2(-3)}$

$=\frac{-5-13}{-6}$

$=\frac{-18}{-6}$

$=3$

Hence, the roots of the given quadratic equation are $-\frac{4}{3}, 3$. 

Tutorialspoint

Updated on: 10-Oct-2022

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