# If the zeroes of the polynomial x3 - 3x2 + x + 1 are a - b, a and a + b respectively, then the values of 'a' and 'b' are respectively.

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DSSSB TGT Maths Female Subject Concerned - 18 Nov 2018 Shift 3
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1. $$1, ±\sqrt{2}$$
2. $$3, -\sqrt2$$
3. $$-1, \sqrt2$$
4. $$1, ± \sqrt{\dfrac{3}{2}}$$

Option 1 : $$1, ±\sqrt{2}$$

## Detailed Solution

Given:

Zeroes of the polynomial = (a - b), a and (a + b)

Formula used:

Sum of zeroes = –B/A

Product of zeroes = -D/A

Where,

A = Coefficient of x3

B = Coefficient of x2

C = Coefficient of x

Calculations:

Using the given polynomial

Sum of zeroes = (a - b) + a + (a + b) = 3

⇒ 3a = 3

⇒ a = 1

Product of zeroes = (a – b) × a × (a + b) = -1

⇒ (1 - b) × 1 × (1 + b) = -1

⇒ 1 - b2 = -1

⇒ b2 = 2

⇒ b = ±√2

∴ The values of 'a' and 'b' are 1 and ±√2