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What is the polynomial roots to 1 5i and -3i?
4
Find all the roots of the polynomial function. f(x)x2-2x-24?
To find the roots of the polynomial function ( f(x) = x^2 - 2x - 24 ), we can factor it or use the quadratic formula. Factoring gives us ( (x - 6)(x + 4) = 0 ). Thus, the roots are ( x = 6 ) and ( x = -4 ). Alternatively, using the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) also yields the same roots.
What second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?
The second-degree polynomial function ( f(x) ) with a lead coefficient of 3 and roots 4 and 1 can be expressed using the factored form: ( f(x) = a(x - r_1)(x - r_2) ), where ( a ) is the lead coefficient, and ( r_1 ) and ( r_2 ) are the roots. Substituting the values, we have ( f(x) = 3(x - 4)(x - 1) ). Expanding this gives ( f(x) = 3(x^2 - 5x + 4) = 3x^2 - 15x + 12 ). Thus, the polynomial is ( f(x) = 3x^2 - 15x + 12 ).
Is the highest degree of any of the terms in the polynomial?
Yes, in a polynomial, the highest degree is determined by the term with the greatest exponent on its variable. For example, in the polynomial (3x^4 + 2x^2 - 5), the highest degree is 4, which comes from the term (3x^4). The degree of a polynomial is significant as it influences the polynomial's behavior and the number of roots it can have.
What is 2X squared minus 7X -4?
The expression (2X^2 - 7X - 4) is a quadratic polynomial in the variable (X). It represents a parabolic function when graphed, with a leading coefficient of 2 indicating that the parabola opens upwards. The roots of this polynomial can be found using the quadratic formula, and it can also be factored if possible.
what are all of the zeros of this polynomial function f(a)=a^4-81?
Find All Possible Roots/Zeros Using the Rational Roots Test f(x)=x^4-81 ... If a polynomial function has integer coefficients, then every rational zero will ...
What is the polynomial roots to 1 5i and -3i?
4
At most how many unique roots will a fourth degree polynomial have?
4, the same as the degree of the polynomial.
Is it true that the degree of polynomial function determine the number of real roots?
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
How many x-intercepts does a quartic polynomial function having 4 distinct real roots have?
Each distinct real root is an x-intercept. So the answer is 4.
Find all the roots of the polynomial function. f(x)x2-2x-24?
To find the roots of the polynomial function ( f(x) = x^2 - 2x - 24 ), we can factor it or use the quadratic formula. Factoring gives us ( (x - 6)(x + 4) = 0 ). Thus, the roots are ( x = 6 ) and ( x = -4 ). Alternatively, using the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) also yields the same roots.
What second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?
The second-degree polynomial function ( f(x) ) with a lead coefficient of 3 and roots 4 and 1 can be expressed using the factored form: ( f(x) = a(x - r_1)(x - r_2) ), where ( a ) is the lead coefficient, and ( r_1 ) and ( r_2 ) are the roots. Substituting the values, we have ( f(x) = 3(x - 4)(x - 1) ). Expanding this gives ( f(x) = 3(x^2 - 5x + 4) = 3x^2 - 15x + 12 ). Thus, the polynomial is ( f(x) = 3x^2 - 15x + 12 ).
Which polynomial has rational coefficients a leading leading coefficient of 1 and the zeros at 2-3i and 4?
There cannot be such a polynomial. If a polynomial has rational coefficients, then any complex roots must come in conjugate pairs. In this case the conjugate for 2-3i is not a root. Consequently, either (a) the function is not a polynomial, or (b) it does not have rational coefficients, or (c) 2 - 3i is not a root (nor any other complex number), or (d) there are other roots that have not been mentioned. In the last case, the polynomial could have any number of additional (unlisted) roots and is therefore indeterminate.
How many real roots can a fourth degree polynomial have?
Upto 4. If the coefficients are all real, then it can have only 0, 2 or 4 real roots.
Is the highest degree of any of the terms in the polynomial?
Yes, in a polynomial, the highest degree is determined by the term with the greatest exponent on its variable. For example, in the polynomial (3x^4 + 2x^2 - 5), the highest degree is 4, which comes from the term (3x^4). The degree of a polynomial is significant as it influences the polynomial's behavior and the number of roots it can have.
What is 2X squared minus 7X -4?
The expression (2X^2 - 7X - 4) is a quadratic polynomial in the variable (X). It represents a parabolic function when graphed, with a leading coefficient of 2 indicating that the parabola opens upwards. The roots of this polynomial can be found using the quadratic formula, and it can also be factored if possible.
What is The largest exponent which is shown in a polynomial is?
The largest exponent in a polynomial is referred to as its degree. The degree of a polynomial indicates the highest power of the variable present in the expression. For example, in the polynomial (3x^4 + 2x^3 - x + 7), the degree is 4, corresponding to the term (3x^4). The degree plays a crucial role in determining the polynomial's behavior and the number of possible roots.
