This question was previously asked in

UP TGT Mathematics 2021 Official Paper

Option 3 : -16

Concept used:

If α and β are the two zeros of the quadratic polynomial ax2 + bx + c, then:

ax2 + bx + c = (x - α)(x - β) = x2 - (α + β)x + αβ = 0

Sum of roots = α + β = −b/a

Product of roots = αβ = c/a

**Formula used:**

a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

a^{2} + b^{2} = (a + b)^{2} - 2ab

Then, a3 + b3 = (a + b)((a + b)2 - 3ab)

**Calculation:**

By comparing the given quadratic equation with the standard quadratic equation we get,

x_{1} + x_{2} = 2 and x_{1}x_{2} = 4

Now, x13 + x23 = (x1 + x2)((x1 + x2)2 - 3x1x2)

⇒ 2(2^{2} - 3 × 4)

⇒ 2(4 - 12)

⇒ 2 × (-8)

⇒ -16