Question

if a and b are zeroes of polynomial 5x^2 + 5x + 1, then find the values of a^2+b^2

Answer 1

Answer:

Step-by-step explanation:

Given : a and b are the zeroes of p(x) = 5x^2+5x+1

need to find a^2 +b^2

A.T.Q

sum of zeroes = -b/a

a+b = -5/5

a+b = -1

now ,

product of zeroes = c/a

a*b = 1/5

ab = 1/5

therefore , we know that (a + b)^2 = a^2 + b^2 +2ab

so, put the value of a+b and ab in the above equation

(-1)^2 = a^2 + b^2 +2*1/5

1 -2/5=a^2 +b^2

5-2/5 =a^2 b^2

3/5 =a^2 b^2

hence , the value of a^2 + b^2 is 3/5 .

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