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# If the zeroes of the polynomial x^{3} - 3x^{2} + x + 1 are a - b, a, a + b, find a and b

**Solution:**

Let us first compare the given polynomial with the general form of the cubic polynomial px^{3} + qx^{2} + rx + t to get the values of p, q, r, and t.

We have, p(x) = x^{3} - 3x^{2} + x + 1

On comparing the given polynomial with px^{3} + qx^{2} + rx + t with x^{3} - 3x^{2} + x + 1, we get, p = 1, q = - 3, r = 1 and t = 1

Given zeroes are a - b, a, a + b.

Sum of zeroes = a - b + a + a + b- coefficient of x^{2} / coefficient of x^{3}

= 3a- q / p = 3a

3 = 3a

a = 1

Since the value of a is found to be 1, the zeroes are 1 - b, 1, 1 + b

Product of zeroes = 1(1 - b)(1 + b) - constant term / coeficient of x³ = 1 - b^{2}- t / p = 1 - b^{2}- 1 / 1 = 1 - b^{2}

1 - b^{2} = - 1

1 + 1 = b^{2}

b^{2} = 2

b = ± √2

Hence, a = 1, b = √2 or - √2

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 2

**Video Solution:**

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

NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.4 Question 3

**Summary:**

If the zeroes of the polynomial x³ - 3x² + x + 1 are a - b, a, a + b, the value of a is 1 and the value of b is √2 or - √2.

**☛ Related Questions:**

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