**Correct option (a) and (d) **

**Explanation:**

α ,β = - b ± √Δ^{2}/2a and β = - b - Δ/2a

or α = -b - Δ/2a and β = - b + Δ/2a

2aα = - b + Δ 2αβ = - b - Δ

2aα + Δ = – b & 2a β - Δ = -b

2aα + Δ = - b + 2Δ

2a β - Δ = -b - 2Δ

S = –2b and P = b^{2 }

∴ S = – 2b and P = + b^{2 }– 4 Δ^{2}

= + b^{2 }– 4(b^{2 }– 4ac)

= –3b^{2 }+ 16ac

∴ quadatic equation is

x^{2 }+ 2bx – 3b^{2 }+ 16ac = 0