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Let Δ2 be the discriminant and α, β be the roots of the equation ax+ bx + c = 0. Then 2aα +  Δ and 2aβ - Δ can be roots of the equation 

(a) x+ 2bx + b2 = 0

(b)  x– 2bx + b2 = 0

(c)  x+ 2bx – 3b– 16ac = 0

(d)  x2+ 2bx–3b+ 16ac = 0 

1 Answer

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Best answer

Correct option (a) and (d) 

Explanation:

α ,β  = - b ± Δ2/2a 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

∴ S = – 2b    and P = + b– 4 Δ2

= + b– 4(b– 4ac)

= –3b+ 16ac

∴ quadatic equation is 

x+ 2bx – 3b+ 16ac = 0

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