If α,β are the roots of 2x2−3x+4=0, then the equation whose roots are α2 and β2 is
A
4x2−7x−16=0
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B
4x2−7x+16=0
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C
4x2+7x+16=0
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D
4x2+7x−16=0
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Solution
The correct option is C4x2+7x+16=0 Let f(x)=2x2−3x+4=0→ roots are α,β
The equation whose roots are α2,β2 is f(√x)=0 ⇒2x−3√x+4=0⇒2x+4=3√x ⇒(2x+4)2=9x⇒4x2+7x+16=0