Question

Solve the quratic equation 2x2 + 5x + 2 = 0 using formula method ​

Answer 1

Given Equation

$\sf\to 2x^2+5x+2=0$

Formula

$\sf\to x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

Now Compare with

$\sf\to ax^2+bx+c=0$

We get

$\sf\to a=1 , b = 5\: and\:c=2$

Put the value on formula

$\sf\to x=\dfrac{-5\pm\sqrt{(5)^2-4\times2\times2} }{2\times2}$

$\sf\to x=\dfrac{-5\pm\sqrt{25-16} }{4}$

$\sf\to x=\dfrac{-5\pm\sqrt{9} }{4}$

$\sf\to x = \dfrac{-5\pm3}{4}$

$\sf\to x=\dfrac{-5+3}{4} \: and \:\dfrac{-5-3}{4}$

$\sf\to x=\dfrac{-2}{4} \: and \: \dfrac{-8}{4}$

$\sf\to x= \dfrac{-1}{2} \:and\: x= -2$

Answer

$\sf\to x= \dfrac{-1}{2} \:and\: x= -2$

Answer 2

Solution:

A quadratic equation is given in this question:

$\displaystyle{\implies\sf\:2x^2+5x+2 = 0}$

We need to solve it by using formula method.

By using formula method, we have:

$\displaystyle{\pink{\sf\:x = \frac{-b \pm \sqrt{D}}{2a}}}$

Here, D represents discriminant of the quadratic equation:

$\displaystyle{\red{\sf\:D = b^2-4ac}}$

where,

• b = 5
• a = 2
• c = 2

$\displaystyle{\implies\sf\:D = 5^2-4\: \times \: 2\: \times \:2 }$

$\displaystyle{\implies\sf\:D = 25-16}$

$\displaystyle{\green{\sf\:D = 9}}$

Now, let us solve the quadratic equation by using quadratic formula:

$\displaystyle{\implies{\sf\:x = \frac{-5 \pm \sqrt{9}}{2\: \times 2}}}$

$\displaystyle{\implies{\sf\:x = \frac{-5 \pm 3}{4}}}$

$\displaystyle{\implies{\sf\:x = \frac{-5 + 3}{4}}}$,$\displaystyle{\implies{\sf\:x = \frac{-5 - 3}{4}}}$

$\displaystyle{\implies{\sf\:x = \frac{-2}{4}}}$,$\displaystyle{\implies{\sf\:x = \frac{-8}{4}}}$

$\displaystyle{\implies{\underline{\boxed{\blue{\sf\:x = \frac{-1}{2},-2}}}}}$

Hence, the quadratic equation is solved!