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Chapter 2 – Polynomials
Important Questions and Solutions
1) The zeros of the quadratic polynomial:
Calculate the value of
Ans – Given,
3) Zeros of the quadratic polynomial 3x2 – kx + 14 are in the ratio 7:6. Calculate the value of ‘k’.
Ans – Let the zeros of the quadratic polynomial, 3x2 – kx + 14 be 7p and 6p.
4) Sum and product of zeros of a quadratic polynomial are ‘a’ and ‘1/a’. Identify the quadratic polynomial.
Ans – A quadratic polynomial is given by:
The sum of zeros is given as => a
The the product of zeros is given as => 1/a
Thus, the quadratic polynomial is:
5) Identify the zeros of the given polynomial:
Ans – The polynomial can be written as:
6) Find the zeros of the polynomial f(x) = 2x3 – 7x2 + 3x + 6 if its two zeros are
Ans – Given the two zeros of the polynomial f(x) = 2x3 – 7x2 + 3x + 6 are:
7) Find the value that must be added to 6x5 + 5x4 + 11x3 – 3x2 + x + 5 so that it can be divided by 3x2 – 2x + 4
Ans – When we divide 6x5 + 5x4 + 11x3 – 3x2 + x + 5 with 3x2 – 2x + 4 we get:
Hence, we need to add 3x2 – 2x + 4 to 6x5 + 5x4 + 11x3 – 3x2 + x + 5 so that it is divisible by 3x2 – 2x + 4.
8) By Division method check whether the polynomial (t2 – 3) is a factor of the polynomial 2t4 + 3t3 – 2t2 – 9t -12
Ans – To check whether the polynomial (t2 – 3) is a factor, we need to divide 2t4 + 3t3 – 2t2 – 9t -12 by (t2 – 3). Thus, we have
=> (t2 – 3) is a factor of the polynomial 2t4 + 3t3 – 2t2 – 9t -12.