good morning everyone i'm joe anderson
from yogi and you today i'm here with a
different question based on polynomials
which is if one zero of a polynomial is
reciprocal of the other find the value
of a from this polynomial in proper
language what is question if one zero of
the polynomial px px s this is
reciprocal of the other then find the
value of a a from this polynomial before
discussing on our answer subscribe my
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videos before we start first we
understand what is the standard form of
quadratic equation standard form of an
quadratic equation is ax square plus BX
plus C here X is unknown variable but
what is a b c a is coefficient of x
square b is coefficient of x and c is
constant term
now our given polynomial is in bracket a
square plus 9x squared plus 13x plus 6ei
by comparing both the polynomials we can
compare the coefficients of x square x
and constant here a is a square plus 9 b
is 13 and sales success if alpha and
beta are zeros of polynomial then it is
given that alpha is reciprocal of beta 1
0 is reciprocal to another by cross
multiplication we get alpha beta is
equal to 1 this is our equation 1 but we
know by the relation of zeros and
coefficients of a polynomial is like
that product of alpha beta means product
of zeros is equal to c upon a c68 and a
is a square plus 9 it is ever equation
number 2 now we can see that left side
of both the equation are same that means
right side is also same so we can write
1 is equal to 6 a upon a square plus 9
by cross multiplication a square plus 9
is equal to 6 a
transferring 6a to left side we can get
this equation a square minus 6a plus 9
by splitting the middle term we get 3a +
3 now by taking a as common from first
to term we get a minus 3 in bracket and
from second two terms by taking 3 we get
a minus 3 in bracket again two terms are
here both the terms has a minus 3 as
common just 8 K minus 3 as common and
what we get remains a minus 3 by
equating both the brackets equal to 0 we
get a is equal to plus 3 and again a is
equal to plus 3 in the last we get
finally a is equal to 3 as the answer so
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