Question

9x^2 + 10x + 3 quatratic equation

Answer 1

9x^2+10x+3

a=9,b=10,c=3

x= -b+-√b^2-4ac/2a

put the values,

-10+-√10^2-4*9*3/2*9

-10+-√100-108/18

-10+-√-8/18

-10+-2/18

-10+2/18 =-8/18=-4/9 Ans

-10-2/18 = -12/18 = -2/3 Ans

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

${\boxed{\bigstar{{Equation\;is\;in\;form\;of:-}}}}$

ax² + bx + c = 0

Here,

a = 9

b = 10

c = 3

${\boxed{\bigstar{{Using\;Formula\;of\; Discriminant}}}}$

b² - 4ac

= (1² - 4 × 1 × 1)

= (1 - 4)

= -3

Here,

-3 < 0

${\boxed{\bigstar{{Equation\;has\;complex\;roots}}}}$

Then,

$\tt{\rightarrow\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$

$\tt{\rightarrow\dfrac{-1\pm \sqrt{1-4}}{2\times 1}}$

$\tt{\rightarrow\dfrac{-1\pm \sqrt{-3}}{2}}$

$\tt{\rightarrow\dfrac{-1\pm i\sqrt{3}}{2}}$

Therefore,

$\tt{\rightarrow\dfrac{-1+i\sqrt{3}}{2}}$

$\tt{\rightarrow\dfrac{-1-i\sqrt{3}}{2}}$