Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Find the roots
[tex]\sf x^2+3x+5=0[/tex]

Use quadratic formula

Note:-

Plagarised/spam/short answers will be deleted on the spot.

Answer with all steps and proper explanation .

Hint:-

irrational roots will come ​


Sagot :

[tex] \sf \: {x}^{2} + 3x + 5 = 0[/tex]

Solve the quadratic equation (ax²+bx+c=0) using the quadratic formula:

[tex] \boxed{ \bf \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }[/tex]

  • a = 1
  • b = 3
  • c = 5

[tex] \tt \: x = \frac{ - 3± \sqrt{ {3}^{2} - 4 \times 1 \times 5 } }{2 \times 1} [/tex]

Any expression multiplied by 1 remains the same

[tex] \tt \: x = \frac{ - 3± \sqrt{ {3}^{2} - 4 \times 5 } }{2} [/tex]

Evaluate the power

[tex] \tt \: x = \frac{ - 3± \sqrt{9 - 4 \times 5} }{2} [/tex]

Multiply the numbers

[tex] \tt \: x = \frac{ - 3± \sqrt{9 - 20} }{2} [/tex]

Calculate the difference

[tex] \tt \: x = \frac{ - 3± \sqrt{ - 11} }{2} [/tex]

Calculate the square root

[tex] \tt \: x = \frac{ - 3± \sqrt{11}i }{2} [/tex]

Write the solutions, one with a + sign and one with a - sign

[tex] \tt \: x = \frac{ - 3 + \sqrt{11} i}{2} \\ \tt \: x = \frac{ - 3 - \sqrt{11}i }{2} [/tex]

Separate the real and the imaginary parts

[tex] \tt \: x = - \frac{3}{2} + \frac{ \sqrt{11} }{2} i \\ \tt \: x = - \frac{3}{2} - \frac{ \sqrt{11} }{2} i[/tex]

∴ The quadratic equation has two solutions

[tex] \rm x_{1} = - \frac{3}{2} + \frac{ \sqrt{11} }{2} i, x_{2} = - \frac{3}{2} - \frac{ \sqrt{11} }{2} i[/tex]

DoYang

Answer:

[tex]⇒x = \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} } - 4ac }{2a} [/tex]

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

[tex]⇒ {x}^{2} + 3x + 5 = 0 \\ ⇒a = 1 \\ ⇒b = 3 \\ ⇒c = 5 \\ ⇒x = \frac{ - 3 \binom{ + }{ - } \sqrt{ {3}^{2} } - 4.1.5}{2.1} [/tex]

▪Evaluate the exponent

▪Multiply the numbers

▪Subtract the numbers

▪Multiply the numbers

[tex]⇒x = \frac{ - 3 \binom{ + }{ - } \sqrt{ - 11} }{2} [/tex]

▪The square root of a negative number is not a real number

[tex]⇒d = - 11[/tex]

no solution

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.