How to find zeros of monomial with 100
Answers
Answer:Finding Zeros of Polynomials
Zeros of a polynomial can be defined as the points where the polynomial becomes zero on the whole. A polynomial having value zero (0) is called zero polynomial. The degree of a polynomial is the highest power of the variable x.
A polynomial of degree 1 is known as a linear polynomial.
The standard form is ax + b, where a and b are real numbers and a≠0.
2x + 3 is a linear polynomial.
A polynomial of degree 2 is known as a quadratic polynomial.
Standard form is ax2 + bx + c, where a, b and c are real numbers and a ≠ 0
x2+ 3x + 4 is an example for quadratic polynomial.
Polynomial of degree 3 is known as a cubic polynomial.
Standard form is ax3+ bx2 + cx + d, where a, b, c and d are real numbers and a≠0.
x3 + 4x + 2 is an example for cubic polynomial.
Similarly,
y6 + 3y4 + y is a polynomial in y of degree 6.
Points to remember:
0 could be a zero of polynomial but it is not necessarily a zero has to be 0 only.
All the linear polynomials have only one zero.
The zeros of the polynomial depends on its degree.
Also, read:
Factorization Of Polynomials
Polynomials Class 9
Polynomial For Class 10
Important Questions Class 10 Maths Chapter 2 Polynomials
Zeros of Polynomial Formula
Consider, P(x) = 4x + 5 to be a linear polynomial in one variable.
Let a be zero of P(x), then,
P(a) = 4k+5 = 0
Therefore, k = -5/4
In general, If k is zero of the linear polynomial in one variable; P(x) = ax +b, then
P(k) = ak+b = 0
k = -b/a
It can also be written as,
Zero of Polynomial K = -(Constant/ Coefficient of x)
Example
Example: What is the value of a if degree of polynomial x3 + xa-4 + x2 + 1 is 4?
Degree of a polynomial P(x) is the highest power of x in P(x).
Therefore, xa-4 = x4
a-4 = 4, a = 4+4 =8
Therefore, the value of a is 8.
In general; if P(x) is a polynomial in x and k is any real number, then the value of P(k) at x = k is denoted by P(k) is found by replacing x by k in P(x).
In the polynomial x2 – 3x + 2,
Replacing x by 1 gives,
P(1) = 1 – 3 + 2 = 0
Similarly, replacing x by 2 gives,
P(2) = 4-6+2 = 0
For a polynomial P(x), real number k is said to be zero of polynomial P(x), if P(k) = 0.
Therefore, 1 and 2 are the zeros of polynomial x2 – 3x + 2.