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2. Polynomials
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Q22 of 109 Page 3

Write a quadratic polynomial, sum of whose zeros is 2√3 and their product is 2.

Given,


Sum of zeros = 2√3 and


Product = 2


As we know;


f(x) = x2 + ( – Sum of zeros)x + (Product of zeros)


So,


f(x) = x2 – 2√3x + 2


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20

State division algorithm for polynomials.

21

Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x) .q(x)+ r(x), where degree r (x) = 0.

23

If fourth degree polynomial is divided by a quadratic polynomial, write the degree of the remainder.

24

If f(x) = x3 + x2 – ax + b is divisible by x2 – x write the values of a and b.

Questions · 109
2. Polynomials
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