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