If the zeroes of the polynomial x3  | Class 10 Mathematics Chapter Polynomials, Polynomials NCERT Solutions

Question:

If the zeroes of the polynomial x– 3x+ 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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Welcome to the NCERT Solutions for Class 10 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 4 , Question 3: If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a a....