Write down the degree of following polynomials in x: 3  2x
Find the degree of the given algebraic expression ax^{2} + bx + c
We know that the degree is the term with the greatest exponent.
If x = 2 and x = 3 are zeroes of the quadratic polynomial x^{2} + ax + b, the values of a and b respectively are
Write the degree of each of the following polynomials: 1 / 2y^{7}  12y^{6} + 48y^{5}  10
3x^{3}  2x  x + 3 is an example of
3x^{3}  2x  x + 3 = 3x^{3}  3x + 3 is an example of cubic polynomials. A cubic polynomial is a polynomial of degree 3. Since the highest degree is 3.
Let p(x) = ax^{2} + bx + c be a quadratic polynomial. It can have at most
The polynomial ax^{2} + bx + c has three terms. The first one is ax^{2}, the second is bx, and the third is c. The exponent of the first term is 2. The exponent of the second term is 1 because bx = bx^{1}. The exponent of the third term is 0 because c = cx^{0}. Since the highest exponent is 2, therefore, the degree of ax^{2} + bx + c is 2. Since, the degree of the polynomial is 2, hence, the polynomial ax^{2} + bx + c can have zero, one or two zeroes. Hence, the polynomial ax^{2} + bx + c can have at most two zeros.
The zero of polynomial p(x) = 4x + 5 is:
To find the zero of a polynomial, we use f(x) = 0.
Then, 4x + 5 = 0 ⟹ 4x = −5 ⟹ x = 5 / 4
Hence, −5 / 4 is the zero of the polynomial 4x + 5.
Draw the graphs of y = x^{2}  x  6 and find the zeroes in each case.
when x = −2; y = 4 + 2 − 6 = 0
when x = 3; y = 9 − 3 − 6 = 0
Assertion: Degree of a zero polynomial is not defined.
Reason: Degree of a nonzero constant polynomial is 0
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively: 0, 3
Find the variable of the linear polynomial t + 5.
Find the zero of the polynomial in each of the following in the following case: p(x) = x +
5
∴ 5 is zero of the polynomial
The variable in the quadratic polynomial t^{2} + 4t + 5 is
What must be subtracted from the polynomial 8x^{4} + 14x^{3} + x^{2} + 7x + (8 so that the resulting polynomial is exactly divisible by 4x^{2}  3x + 2?
Thus, when 6x + 2 is subtracted from the given polynomial 8x^{4} + 14x^{3} + x^{2} + 7x + 8, then it will be divisible by 4x^{2}  3x + 2.
Classify the following polynomial based on their degree: 3x^{2} + 2x + 1
where a_{n}, a_{n−1},... a_{2}, a_{1}, a_{0}. are constants and n is a natural number.
Let p(x) = 3x^{2} + 2x + 1
The degree of a polynomial is the highest power of x in its expression.
Constant (nonzero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, 2 , 3 and 4 respectively.
Highest power of x in p(x) is = 2
Thus, the degree of p(x) is 2.
Hence, it is a quadratic polynomial.
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