Question

Find the roots of quadratic equation if exists 2x2 +3x+10=0.

Answer 1

Answer:

For existence of root , First we find the discriminant (D)

D = b² - 4ac

= 3² - 4×2×10

= 9 - 80

= -71 .

Since the discriminant is negative so root will be imaginary .

x = -b+- √D/2a

x = -3 -i√71 /4 or -3+i√71/4

Hope you understand

Answer 2

2x² + 3x + 10 = 0

here , [ a = 2 , b = 3 , c = 10 ]

finding Roots by Quadratic formula :-

$\huge \rm root s = \frac{ {b}^{2} \pm \sqrt{ {b}^{2} - 4ac \: } }{2a}$

so ,

$\rm \alpha (or) \beta = \frac{ {3}^{2} \pm \sqrt{ {(3)}^{2} - 4(2)(10)} }{2(2)} \\ \\ \\ = \frac{9 \pm \sqrt{9 - 40} }{4} = \frac{9 \pm \sqrt{31} }{4} \\ \\ \rm so \: \: \orange{\underline{ \pink{ \: \: roots \: \: \: \: are \: \: \: : \: \: \: }}} \\ \\ \\ \sf \blue{\boxed{ \sf\frac{9 + \sqrt{31} }{4} }}\: \: \: \: and \: \: \: \: \red{ \boxed{ \frac{ \sf9 - \sqrt{31} }{4} }}$