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Polynomials

Question
CBSEENMA10006087
Wired Faculty App

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
      4 straight s squared minus 4 straight s plus 1
     

Solution
We have,
4s2 – 4s + 1 = 4s2 – 2s –2s + 1 = (2s–1)(2s– 1)
So, the value of 4s2 – 4s + 1 is zero, when 2s – 1 = 0 or 2s – 1 = 0
i.e.  when   straight s equals 1 half space or space straight s equals 1 half
Therefore, the zeroes of 4s2 – 4s + 1 are 1 half space and space 1 half. Now,
     Sum of zeroes =  1 half plus 1 half
                             equals 1 over 1 equals fraction numerator negative left parenthesis Coefficient space of space straight s right parenthesis over denominator Coefficient space of space straight s squared end fraction
Product of zeroes  = 1 half cross times 1 half equals 1 fourth
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Some More Questions From Polynomials Chapter

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x3 – 3x2 + 5x – 3,    g(x) = x2 – 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x4 – 3x2 + 4x + 5,      g(x) = x2 + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
p(x) = x4 – 5x + 6,      g(x) = 2 – x2.

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
t2 – 3,  2t4 + 3t3 – 2t2–9t – 12

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