Q5 of 227 Page 114

If α, β are roots of 2x2 – 3x – 5 = 0, from an equation whose roots are α2 and β2.

2x2 – 3x – 5 = 0 compare this with ax2 – bx + c = 0


∴ a = 2 , b = –3 and c = –5








Here α = α2 and β = β2


General form of quadratic equation whose roots are α2 and β2


⇒ x2 – (α2 + β2) x + α2β2 = 0


⇒ x2 – (α2 + β2) x + (αβ)2 = 0


α2 + β2 = (α + β)2 – 2(αβ)





x2 – (α2 + β2) x + (αβ)2 = 0





4x2 – 29x + 25 = 0


Therefore the required equation is 4x2 – 29x + 25 = 0


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