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if x-2 and x-1/2 are factors of px² +5x+r then show that p=r

Asked by vrishti TOKAS | 18th Jun, 2015, 08:24: PM

Expert Answer:

$f left parenthesis x right parenthesis equals p x squared plus 5 x plus r left parenthesis x minus 2 right parenthesis space a n d space open parentheses x minus 1 half close parentheses space a r e space t h e space f a c t o r s space o f space f left parenthesis x right parenthesis f left parenthesis 2 right parenthesis equals 0 4 p plus 10 plus r equals 0.......... left parenthesis i right parenthesis f open parentheses 1 half close parentheses equals 0 p cross times 1 fourth plus 5 cross times 1 half plus r equals 0 fraction numerator p plus 10 plus 4 r over denominator 4 end fraction equals 0 p plus 4 r plus 10 equals 0.......... left parenthesis i i right parenthesis left parenthesis i right parenthesis space cross times 4 minus left parenthesis i i right parenthesis rightwards double arrow 16 p plus 4 r plus 40 minus p minus 4 r minus 10 equals 0 rightwards double arrow 15 p plus 30 equals 0 rightwards double arrow 15 p equals negative 30 therefore p equals negative 2 left parenthesis i right parenthesis space rightwards double arrow 4 p plus 10 plus r equals 0 rightwards double arrow 4 left parenthesis negative 2 right parenthesis plus 10 plus r equals 0 rightwards double arrow r plus 2 equals 0 therefore r equals negative 2 F r o m space t h e space v a l u e s space o f space p space a n d space r comma space w e space c a n space s a y space t h a t space p equals r$

Answered by Prasenjit Paul | 19th Jun, 2015, 10:47: AM

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