is the square root of m 7 a polynomial Algebra Simplify square root of m 7 m7 m 7 Rewrite m7 m 7 as m3 2 m m 3 2 m Tap for more steps m3 2 m m 3 2 m Pull terms out from under the radical m3 m
When we use a radical sign and write sqrt m it denotes the positive square root of m The positive square root is also called the principal square root If We can generalise this approach in order to find rational roots Consider the polynomial 6x 2 x 2 text We can find its zeros using the quadratic formula
is the square root of m 7 a polynomial
is the square root of m 7 a polynomial
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The fundamental theorem of algebra states that a polynomial P z of degree n has n roots some of which may be degenerate For example the roots of the polynomial x 3 2x 2 x 2 x Numbers like Pi or a square root that contains a real number that is not a perfect square would be irrational numbers Now if you had an expression 5 2 x 2 it would be a polynomial with a coefficient that is an irrational number
1 If the coefficients of a polynomial are real and if a ib is a root of that polynomial then so is a ib See Complex Conjugate Root Theorem 2 If a polynomial with rational coefficients has a sqrt b as a We can take a polynomial such as f x ax n bx n 1 cx n 2 z And then factor it like this f x a x p x q x r Then p q r etc are the roots where the polynomial equals zero Quadratic Let s try this with a
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Square root of polynomial The f f denoted by f f is any polynomial g g having the square g2 g 2 equal to f f For example 9x2 30x 25 3x 5 9 x 2 30 x First we ll graph the polynomial to see if we can find any real roots from the graph We can see in the graph that this polynomial has a root at x frac 4 3 That means that the polynomial must have a factor of 3
Therefore the square root of the given polynomial is 3x2 x 1 Example 4 Find the square root of the following polynomial 4 25x2 12x 24x3 16x4 Solution First To solve this you would end take the square root of a negative and just as you would with the square root of a positive you would have to consider both the positive and negative
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is the square root of m 7 a polynomial - We earlier defined the square root of a number in this way If n 2 m then n is a square root of m Since these equations are all of the form x 2 k the square root