Question

solve the following quadratic equations
using
formula:
2x² + x-1÷5 =0​

Answer 1

SolutioN :

We have,

$\tt \dagger \: \: \: \: \: 2 {x}^{2} + x - \dfrac{1}{5} = 0.$

$\tt : \implies 2 {x}^{2} + x - \dfrac{1}{5} = 0.$

$\tt : \implies \dfrac{10 {x}^{2} + 5x - 1 }{5} = 0.$

$\tt : \implies 10 {x}^{2} +5 x -1 = 0.$

★ Compare with General Equation.

$\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c = 0.$

Where as,

• a = 10.
• b = 5.
• c = - 1.

Now,

$\tt : \implies x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\tt : \implies x = \dfrac{ - 5\pm \sqrt{ {5}^{2} - 4 \times - 1 \times 10 } }{2 \times 10}$

$\tt : \implies x = \dfrac{ - 5 \pm \sqrt{ 25 + 40} }{20}$

$\tt : \implies x = \dfrac{ - 5 \pm \sqrt{ 65 } }{10}$

Therefore, the value of x = - 5 ± √65 / 10.