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Question

If sum of the squares of zeroes of the quadratic polynomialf(x)=x28x+k is 40, find the value of K.

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Solution


Let a and b be the zeroes of the polynomial f(x)=x28x+k. Then,
a+b=(81)=8 and ab=K1=K
It is given that
a2+b2=40
=(a+b)22ab=40
=822K=40
=2K=6440
K=12

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