Question

*Solve the quadratic equation by using formula x^2 + 10 x + 2 = 0* 1️⃣ (-5 - √23 and -5 - √23 ) 2️⃣ (5 + √23 and 5 - √23 ) 3️⃣ (-5 + √23 and -5 + √23 ) 4️⃣ (-5 + √23 and -5 - √23 )​

Answer 1

Answer:

Solve quadratic equations using formula. x2 + 10x + 2 = 0

Step-by-step explanation:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Solve the quadratic equation by using formula x² + 10 x + 2 = 0

1. (-5 - √23 and -5 - √23 )

2. (5 + √23 and 5 - √23 )

3. (-5 + √23 and -5 + √23 )

4. (-5 + √23 and -5 - √23 )

CONCEPT TO BE IMPLEMENTED

SRIDHAR ACHARYYA formula

For any quadratic equation

$a {x}^{2} + bx + c = 0$

The roots are given by

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

EVALUATION

Here the given Quadratic equation is

x² + 10x + 2 = 0

We solve it by Sridhar Acharya formula as below

Comparing with the general equation

ax² + bx + c = 0 we get

a = 1 , b = 10 , c = 2

Hence the required roots

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

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

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

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

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

$\displaystyle \sf{ = - 5 \pm \: 2\sqrt{ 23} }$

FINAL ANSWER

Hence the correct option is

4. (-5 + √23 and -5 - √23 )

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