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If the zeroes of the polynomial x 3 – 3x 2 + x + 1 are a – b, a, a + b, then find the value of a and b

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Let the given polynomial be:

p(x) = x^3– 3x^2+ x + 1

Given,

The zeroes of the p(x) are a – b, a, and a + b.

Now, compare the given polynomial equation with general expression.

px^3+ qx^2+ rx + s = x^3– 3x^2+ x + 1

Here, p = 1, q = -3, r = 1 and s = 1

For sum of zeroes:

Sum of zeroes will be = a – b + a + a + b

-q/p = 3a

Substitute the values q and p.

-(-3)/1 = 3a

Or,
a = 1

So, the zeroes are 1 – b, 1, 1 + b.

For the product of zeroes:

Product of zeroes = 1(1 – b)(1 + b)

-s/p = 1 – 𝑏^2

=> -1/1 = 1 – 𝑏^2

Or, 𝑏^2= 1 + 1 =2

So,
b = √2

Thanks

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