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Maths-

General

Easy

Question

A quadratic equation f(x) = ax²+ bx + c = 0 has positive distinct roots reciprocal of each other .Which one is correct ?

f'(1)=0
af'(1)< 0
c $\neq$ 0
abc $\neq$ 0

The correct answer is: af'(1)< 0

$table row cell alpha plus fraction numerator 1 over denominator alpha end fraction greater than 2 rightwards double arrow fraction numerator negative b over denominator a end fraction greater than 2 rightwards double arrow fraction numerator 2 a plus b over denominator a end fraction less than 0 end cell row cell rightwards double arrow a left parenthesis 2 a plus b right parenthesis less than 0 rightwards double arrow a f to the power of ´ end exponent left parenthesis 1 right parenthesis less than 0 end cell end table$

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The Maxwell's four equations are written as:
i) $not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top equals fraction numerator q subscript 0 end subscript over denominator epsilon subscript 0 end subscript end fraction$
ii) $not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals 0$
iii) $not stretchy contour integral stack E with rightwards arrow on top. stack d l with rightwards arrow on top equals fraction numerator d over denominator d t end fraction not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top$
iv) $not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals mu subscript 0 end subscript epsilon subscript 0 end subscript fraction numerator d over denominator d t end fraction not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top$
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i) $not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top equals fraction numerator q subscript 0 end subscript over denominator epsilon subscript 0 end subscript end fraction$
ii) $not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals 0$
iii) $not stretchy contour integral stack E with rightwards arrow on top. stack d l with rightwards arrow on top equals fraction numerator d over denominator d t end fraction not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top$
iv) $not stretchy contour integral stack B with rightwards arrow on top. stack d s with rightwards arrow on top equals mu subscript 0 end subscript epsilon subscript 0 end subscript fraction numerator d over denominator d t end fraction not stretchy contour integral stack E with rightwards arrow on top. stack d s with rightwards arrow on top$
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