Question

Find the roots of the quadratic equation
2x² 5x+3=0 by applying
the quadratic
formula​

Answer 1

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Question :

Find the roots of the quadratic equation 2x²-5x+3=0 by applying the formula method :

To find :

Root of given quadratic equation =?

Given equation :

2x²-5x+3

Formula :

$\blue \bigstar \large \boxed { \sf{ \underline{ \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} \: \: \: \: \: \: ......formula \: method}}}$

Solution :

$\diamondsuit \bf \: 2 {x}^{2} - 5x + 3 = 0 \: ....given \: quadratic \: equation \:$

➡ a=2

➡ b=-5

➡ c=3

$\\ \implies \green{\bold{ \underline { \ by \: using \: determinant \: method}}}$

$\implies \large \sf \: {b}^{2} - 4ac \:$

$\implies \large\sf {( - 5)}^{2} - 4(2)(3)$

$\implies \large \sf \: 25 - 24 = \boxed{1}$

$\\ \implies \green{ \bold{ \underline{by \: using \: formula \: method}}}$

$\\ \implies \large \sf \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

$\\ \implies \large \sf \: x = \frac{ - ( - 5) \pm \: 1}{2 \times 2}$

$\\ \implies \large \sf \: x = \frac{5 \pm \: 1}{4}$

$\\ \implies \large \sf \: x = \frac{5 + 1}{4} \: \: \: \: \: and \: \: \: x = \frac{5 - 1}{4}$

$\\ \implies \large \sf \: x = \frac{6}{4} \: \: and \: \: x = \frac{4}{4}$

$\\ \implies \large \sf \: \boxed{x = \frac{3}{2}} \: \: and \: \boxed{x = 1 }$

$\therefore \red{\bold{ \underline{roots \: are \: \: x = \frac{3}{2} \: \: and \: \: x = 1}}}$

Answer 2

2x^2 + 5x + 3 = 0

$d = {b}^{2} - 4ac$

a = 2 , b = 5 , c = 3

d = 5^2 - 4 × 2 × 3

d = 25 - 24

d = 1

= - b _+√d/2a

= - 5 _+ √1/2×2

= - 5 +√1/4 = -5 +1/4 = -4/4 = -1 ( i )

= -5 -√1/4 = -5 -1 / 4 = -6/4 = -3/2 ( ii )