Question

obtain the roots of the following equations by using the general formula for the solution:
$9 {x}^{2} + 7x - 2 = 0$
​

Answer 1

Given

A quadratic equation

$\sf\\bullet\red{9 {x}^{2} + 7x - 2 = 0}$

To find

• roots
• By general formula

Solution

$\sf\bullet\red{9 {x}^{2} + 7x - 2 = 0}$

a= 1

b=7

c=-2

Quadratic formula

• $\boxed{\boxed{\sf\red{\bullet{X=\dfrac{-b\pm\Sqrt{d}}{2a}}}}$

$\boxed{\boxed{\sf\red{\bullet{D}=b^2-4ac}}}$

$\implies\sf{D}=49+8</p><p></p><p>[tex]\therefore\sf{D}=57</p><p></p><p></p><h3><u>Now putting values in quadratic formula</u></h3><p></p><p></p><p>[tex]\boxed{\boxed{\sf\red{\bullet{X}=\dfrac{-b\pm\Sqrt{d}}{2a}}}}$

$\boxed{\boxed{\sf\red{\bullet{\rightarrow\:X=\dfrac{-7\pm\Sqrt{d</p><p>57}}{2}}}}$

Taking X =+

$\boxed{\boxed{\sf\red{\bullet{\rightarrow\:X=\dfrac{-7+\Sqrt{</p><p>57}}{2}}}}[/tex<u>]</u></p><p></p><p></p><h3><u>Taking</u><u> </u><u>X</u><u> </u><u>=</u><u> </u><u>-</u></h3><p></p><p></p><p>[tex]\boxed{\boxed{\sf\red{\bullet{\rightarrow\:X=\dfrac{-7-\Sqrt{</p><p>57}}{2}}}}$