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CBSE Class 10 Answered

If a, a+b, a+2b are the zero of the cubic polynomial f(x) =x^3 -6x^2+3x+10 then find the value of a and b as well as all zeros of polynomial.    
Asked by guptaabhinav0809 | 19 Nov, 2018, 10:38: PM
answered-by-expert Expert Answer
begin mathsize 12px style f left parenthesis x right parenthesis space equals space x cubed minus 6 space x squared plus 3 x space plus 10 space................... space left parenthesis 1 right parenthesis

l e t space p comma space q space a n d space r space a r e space z e r o s space o f space p o l y n o m i a l space f left parenthesis x right parenthesis

f left parenthesis x right parenthesis space equals space left parenthesis x minus p right parenthesis left parenthesis x minus q right parenthesis left parenthesis x minus r right parenthesis space equals space x cubed space minus space left parenthesis p plus q plus r right parenthesis space x squared space plus left parenthesis space p q space plus space q r space plus space r p right parenthesis space x space minus space p q r space.......... left parenthesis 2 right parenthesis

b y space c o m p a r i n g space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space g e t

p plus q space plus space r space equals space 6 space space space space space.............. left parenthesis 3 right parenthesis
p q space plus space q r space plus space r p space equals space 3 space space............... left parenthesis 4 right parenthesis
space p q r space equals space minus 10 space space................. left parenthesis 5 right parenthesis

b y space s o l v i n g space e q n s. space left parenthesis 3 right parenthesis comma space left parenthesis 4 right parenthesis space a n d space left parenthesis 5 right parenthesis space w e space g e t comma space space space space space space space p equals 5 comma space q space equals 2 space space a n d space space r space equals space minus 1 space

end style

since p, q, r are in arithmetic progression with initial value 5 and common difference -3  and
the required values a, a+b abd a+2b are also in arithmetic progression with initial value a and common difference b, 
 
a = 5, b = -3
 
zeors of polynomial are 5, 2 and -1
Answered by Thiyagarajan K | 20 Nov, 2018, 02:47: AM
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