If the zeroes of the polynomial x³ - 3x² + 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  px³ + qx² + rx + t to get the values of p, q, r, and t.

We have, p(x) = x³ - 3x² + x + 1

On comparing the given polynomial with px³ + qx² + rx + t with x³ - 3x² + 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 x² / coefficient of x³ 

= 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 - b²- t / p = 1 - b²- 1 / 1 = 1 - b²

1 - b² = - 1

1 + 1 = b²

b² = 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.

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