SELECT * FROM question_mgmt as q WHERE id=9509 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=9 AND subId=6 AND chapterId=269 and ex_no='4' AND status=1 ORDER BY CAST(question_no AS UNSIGNED) CBSE Free NCERT Solution of 10th mathematics Polynomials if the zeroes of the polynomial x3 nbsp ndash 3x

Question:

If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b.

Answer:

Given, p(x) = x3 - 3x2 + x + 1

And zeroes are given as a – b, a, a + b

Now, comparing the given polynomial with general expression, we get;

∴ ax3+bx2+ cx + d = x3 – 3x2+ x + 1

a = 1, b = -3, c = 1 and d = 1

Sum of zeroes = a – b + a + a + b

-b/a = 3a

Putting the values b and a

- (-3)/1 = 3a

                a = 1

Thus, the zeroes are 1 - b, 1, 1 + b.

Now, product of zeroes = 1(1 – b) (1 + b)

d/a = 1 - b2

-1/1 = 1- b2

b2 = 1 + 1 = 2

b = √2

Hence, 1, -√2, 1, 1 + √2 are the zeroes of x3 – 3x2 + x + 1


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