If α and β are the roots of ax^2 + bx + c = 0, then what is the value of [1/{\alpha^2}-1/{\beta^2}]^2?

Correct Answer is : b2(b2−4ab)c4

\frac{b^ 2 (b^ 2 - 4 ab) }{c^4 }

RRB NTPC Mains or Stage 2 Model Paper 4 with solutions

Question : 20 of 120

Marks: +1, -0

If α and β are the roots of

ax^2 + bx + c = 0,

then what is the value of

[1/{α^2}-1/{β^2}]^2?

Solution:

(a) α and β are the roots of the equation

ax^2 +bx + c = 0

∴ α + β-b/a and αβ=c/a

∴[1/{α^2 }-1/{β^2}]^ 2 =[{β^2-α^2} /{α^2β^ 2}] ^2

{(α+β)^2 (α+β )^2-4αβ }/{(α^2β^2 )^2}

={ b^2}/{a^2} [{b ^2}/{a^2}-{4c}/ a]/{c^2}/{a^2}

={b^2}/{c^4}(b^2-4ac)

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