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Polynomials

Question
CBSEENMA10006084
Wired Faculty App

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
     straight x squared minus 2 straight x minus 8

Solution

We have,
      space space space straight x squared minus 2 straight x minus 8 space equals space straight x squared minus 4 straight x plus 2 straight x minus 8
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So, the value of x2 – 2x - 8 is zero when x - 4 = 0 or x + 2 = 0.
i.e., when x = 4 or x = –2.
Therefore, the zeroes of x2 – 2x – 8 are 4 and - 2. Now,
   Sum of zeroes = (4) + (-2)
                           equals 2 over 1 equals fraction numerator negative left parenthesis Coefficient space of space straight x right parenthesis over denominator Coefficient space of space straight x squared end fraction
Product of zeroes = (4) (-2)
                             equals fraction numerator negative 8 over denominator 1 end fraction equals fraction numerator Constant space term over denominator Coefficient space of space straight x squared end fraction.

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

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