anonymous
  • anonymous
What is the degree of 12x^2 + 5x^4 - 2?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
3
anonymous
  • anonymous
3 isn't one of the options :( there's 2 or 4?
UnkleRhaukus
  • UnkleRhaukus
What is the higest power of x ?

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anonymous
  • anonymous
oh sorry its 2 mybad
anonymous
  • anonymous
Solve for x over the real numbers: 5 x^4+12 x^2-2 = 0 Simplify 5 x^4+12 x^2-2 = 0 by making a substitution. Substitute y = x^2: 5 y^2+12 y-2 = 0 Write the quadratic equation in standard form. Divide both sides by 5: y^2+(12 y)/5-2/5 = 0 Solve the quadratic equation by completing the square. Add 2/5 to both sides: y^2+(12 y)/5 = 2/5 Take one half of the coefficient of y and square it, then add it to both sides. Add 36/25 to both sides: y^2+(12 y)/5+36/25 = 46/25 Factor the left hand side. Write the left hand side as a square: (y+6/5)^2 = 46/25 Eliminate the exponent on the left hand side. Take the square root of both sides: y+6/5 = sqrt(46)/5 or y+6/5 = -sqrt(46)/5 Look at the first equation: Solve for y. Subtract 6/5 from both sides: y = sqrt(46)/5-6/5 or y+6/5 = -sqrt(46)/5 Perform back substitution on y = sqrt(46)/5-6/5. Substitute back for y = x^2: x^2 = sqrt(46)/5-6/5 or y+6/5 = -sqrt(46)/5 Eliminate the exponent on the left hand side. Take the square root of both sides: x = sqrt(sqrt(46)/5-6/5) or x = -sqrt(sqrt(46)/5-6/5) or y+6/5 = -sqrt(46)/5 Look at the third equation: Solve for y. Subtract 6/5 from both sides: x = sqrt(sqrt(46)/5-6/5) or x = -sqrt(sqrt(46)/5-6/5) or y = -6/5-sqrt(46)/5 Perform back substitution on y = -6/5-sqrt(46)/5. Substitute back for y = x^2: x = sqrt(sqrt(46)/5-6/5) or x = -sqrt(sqrt(46)/5-6/5) or x^2 = -6/5-sqrt(46)/5 Show the equation has no solution. x^2 = -6/5-sqrt(46)/5 has no solution since for all x on the real line, x^2 >=0 and -6/5-sqrt(46)/5ɘ: Answer: | | x = sqrt(sqrt(46)/5-6/5) or x = -sqrt(sqrt(46)/5-6/5)
UnkleRhaukus
  • UnkleRhaukus
you do not have to solve the equation to find its degree
anonymous
  • anonymous
Degree = the highest power on the variable in this case its 4

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