Question

14. Show that 2,- 1 and
1/2

are the zeroes of the
cubic polynomial p(x)=
2x³- 3x²-3x + 2
and then verify that the sum of the zeroes
=- coefficient of x²/
coefficient of x³

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Answer 1

Answer:

substitute the given zeroes and check

i) p(x) = 2x³-3x²-3x+2

p(2) = 2(2)³-3(2)²-3(2)+2 = 16-12-6+2 = 10-10 = 0

so (2) is the first zero which is alpha(A)

ii) p(-1) = 2(-1)³-3(-1)²-3(-1)+2 = -2-3+3+2 = 0

so (-1) is the second zero which is beta(B)

iii) p(1/2) = 2(1/2)³-3(1/2)²-3(1/2)+2 = (1/4)-(3/4)-(3/2)+2 = 1/2-1/2 = 0

so even 1/2 is the third zero which gama(G)

the relation of the zeroes is their sum = - (coefficient of x²)/(coefficient of x³) which is -b/a

= -(-3)/2 = 3/2 on LHS

then on RHS there is sum of zeroes

= 2+(-1)+1/2 = (4+(-2)+1)/2 because LCM is 2

= 3/2

therefore RHS = LHS the zeroes are verified

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