Question

Find a quadratic polynomial whose sum and product of zeroes is √2 and -3/2 respectively . Also, find its zeroes

Answer 1

Answer:

zeros of quadratic polynomial f(x) are know, then find required polynomial by following formula 

Let f(x)=k{x2−(sum of zeros)+x+product of zeros}, 

where k=a real number

Let f(x) be a polynomial

Sum and product of whose zeros are −3 and 2 respectively

f(x)=k[x2−(−3)x+2]=k[x2+3x+2] (∵k=real number)

Thus required polynomial f(x)=x2+3x+2

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