Question

Solve the following equation by formala method.
x^2 + 10x + 2 = 0​

Answer 1

The roots of the given quadratic equation are - 5 + √23 and - 5 - √23.

Given :

The equation x² + 10x + 2 = 0

To find :

The roots of the quadratic equation by formula method

Concept :

A general equation of quadratic equation is

ax² + bx + c = 0

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation ax² + bx + c = 0

The roots are given by

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

Solution :

Step 1 of 3 :

Write down the given Quadratic equation

Here the given Quadratic equation is

x² + 10x + 2 = 0

Step 2 of 3 :

Write down the coefficients

Comparing the given quadratic equation with general form of quadratic equation ax² + bx + c = 0 We get

a = 1 , b = 10 , c = 2

Step 3 of 3 :

Find the roots of the quadratic equation

By Sridhar Acharyya formula the roots are given by

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

$\implies \: \displaystyle \sf x = \frac{ - 10\pm \: \sqrt{ {( 10)}^{2} - 4 \times 1 \times 2 } }{2 \times 1}$

$\implies \: \displaystyle \sf x = \frac{ - 10 \pm \: \sqrt{100 - 8 } }{2}$

$\implies \: \displaystyle \sf x = \frac{ - 10 \pm \: \sqrt{ 92 } }{2}$

$\implies \: \displaystyle \sf x = \frac{ - 10\pm \: 2\sqrt{ 23 } }{2}$

$\implies \: \displaystyle \sf t = { - 5\pm \: \sqrt{ 23 } }$

Hence roots of the given quadratic equation are - 5 + √23 and - 5 - √23.

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