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Let p(x) = ax2 + bx + c be a quadratic polynomial. It can have at most
Detailed Solution for Test: Polynomials (Easy) - Question 6
The polynomial ax2 + bx + c has three terms. The first one is ax2, 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 = bx1. The exponent of the third term is 0 because c = cx0. Since the highest exponent is 2, therefore, the degree of ax2 + bx + c is 2. Since, the degree of the polynomial is 2, hence, the polynomial ax2 + bx + c can have zero, one or two zeroes. Hence, the polynomial ax2 + bx + c can have at most two zeros.
Assertion: Degree of a zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is 0
Detailed Solution for Test: Polynomials (Easy) - Question 9
We know that, The constant polynomial 0 is called a zero polynomial. The degree of a zero polynomial is not defined, a Assertion is true. The degree of a non-zero constant polynomial is zero. A Reason is true. Since both Assertion and Reason are true and Reason is not a correct explanation of Assertion. The correct answer is B.
Classify the following polynomial based on their degree: 3x2 + 2x + 1
Detailed Solution for Test: Polynomials (Easy) - Question 15
A polynomial is a function of the form f(x) = anxn + an−1xn−1 +...+ a2x2 + a1x + a0
where an, an−1,... a2, a1, a0. are constants and n is a natural number.
Let p(x) = 3x2 + 2x + 1
The degree of a polynomial is the highest power of x in its expression.
Constant (non-zero) 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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