how many roots does x 2 have The Fundamental Theorem of Algebra says a polynomial of degree n has n roots Nowhere does it say the roots must be unequal Every equation x 2 a has the roots x a The roots might be real and unequal real and equal or a pair of complex conjugates In the case of x 2 0 you take the square root on both sides x 2 0 x
An obvious solution is x 2 If 2x x2 then x 1 and x 0 I ll treat the positive and negative cases separately If x 0 then we get xln 2 2ln a or x lnx 2 ln2 The derivative of g x x lnx is lnx 1 lnx 2 In plain English this theorem says that the degree of a polynomial equation tells you how many roots the equation will have A linear equation degree 1 will have one root A quadratic equation degree 2 will have two roots A cubic equation degree 3 will have three roots
how many roots does x 2 have
how many roots does x 2 have
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Roots You Can Eat TasteWise Kids
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The fundamental theorem of algebra says a degree n polynomial has n roots counted with multiplicity x 2 has 1 root 0 with multiplicity 2 Stated another way every degree n polynomial factors as a x r1 x r2 x rn where ax n is the leading term a is non zero and r1 rn are complex numbers Note complex numbers include real numbers The discriminant is b 2 4ac which comes from the quadratic formula and we can use this to find the nature of the roots
Polynomial roots calculator This free math tool finds the roots zeros of a given polynomial The calculator computes exact solutions for quadratic cubic and quartic equations Calculator shows all the work and provides step by step on how to find zeros and their multiplicities With x 2 3x 2 the assumption that the roots be positive holds and the modified equation x 2 3 x 2 has four real roots pm 1 pm 2 However with x 2 x 2 that assumption does not hold and here the modified equation x 2 x 2 has two real roots pm 1
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According to the fundamental theorem of algebra how many roots does the polynomial f x x 4 3x 2 7 have over the complex numbers and counting roots with multiplicity greater than one as distinct i e f x x 2 has two roots both are zero Polynomials have roots zeros where they are equal to 0 Roots are at x 2 and x 4 It has 2 roots and both are positive 2 and 4 Sometimes we may not know where the roots are but we can say how many are positive or negative just
The Fundamental Theorem of Algebra can be used in order to determine how many real roots a given polynomial has Check it out Solve quadratic equations using a quadratic formula calculator Calculator solution will show work for real and complex roots Uses the quadratic formula to solve a second order polynomial equation or quadratic equation Shows work by example of the entered equation to find the real or complex root solutions
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how many roots does x 2 have - We can see that there is a root at x 2 This means that the polynomial will have a factor of x 2 We can use Synthetic Division to find any other factors Because x 2 is a root we should get a zero remainder So now we know that 2 x 3 3 x 2 2 x 8 x 2 left 2 x 2 x 4 right