Polynomials online mcq quiz
Polynomials boostup points
If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x)
➦Types of Polynomials
⤍ A polynomial of degree 1 is called a linear polynomial.
⤍ A polynomial of degree 2 is called a quadratic polynomial.
⤍ A polynomial of degree 3 is called a cubic polynomial.
➦ Zeroes of a Polynomial
⤍ If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).
⤍ A real number k is said to be a zero of a polynomial p(x), if p(k) = 0.
⤍ Geometrical Meaning of Zeroes of Polynomials
⤍The equation ax2 + bx + c can have three cases for the graphs
⤍ Case (i): Here, the graph cuts x-axis at two distinct points A and A′.
⤍ Case (ii): Here, the graph cuts the x-axis at exactly one point
⤍ Case (iii): Here, the graph is either completely above the x-axis or completely below the x-axis.
➦ Relationship between Zeroes and Coefficients of a Polynomial
⤍ If α and β are the zeroes of the quadratic polynomial p(x) = ax2+ bx + c, a 0, then you know that x − α and x − β are the factors of p(x).
⤍ α + β = − b/a
⤍ αβ = c/a
⤍ If p(x) and g(x) are any two polynomials with g(x) 0, then we can find polynomials q(x) and r(x) such that p (x) = g(x) × q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).
⤍ This result is known as the Division Algorithm for polynomials.
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