This question was previously asked in

UPSSSC Chakbandi Lekhpal Official Paper 2 (Held on : 30 Sept 2019 Shift 2)

Option 4 : cx2 + bx + a = 0

**Given:**

For a quadratic equation of form (ax2 + bx + c) = 0,

Sum of roots = - b/a

Product of roots = c/a

**Calculation:**

Roots of equation are ‘α' and ‘β’,

⇒ (α + β) = - b/a

⇒ αβ = c/a

Now,

⇒ 1/α, 1/β are the roots

⇒ (α + β) = (1/α + 1/β) = (α + β)/αβ = - b/c ----(1)

⇒ αβ = 1/αβ = a/c ----(2)

x^{2} - (α + β)x + αβ = 0 ----(3)

When we substitute (1) & (2) in (3)

x^{2 }+ (b/c)x + (a/c) = 0

Divide c from both sides,

cx2 + bx + a = 0

**∴ cx2 + bx + a = 0 is the quadratic equation whose roots are 1/α and 1/β. **