Question

If a and b are zeroes of the polynomial f(x)=x²-4x-5 then find the value of a²+b²​

Answer 1

Answer:

${x}^{2} - 4x - 5 = 0 \\ \\ {x}^{2} + x - 5x - 5 = 0 \\ \\ x(x + 1) - 5(x + 1) = 0 \\ \\ (x + 1) \: (x - 5) = 0 \\ \\ x = - 1 \: (say \: \: a) \\ \\ or \: x = 5 \: (say \: b)$

Now,

${a}^{2} + {b}^{2} = {( - 1)}^{2} + {(5)}^{2} \\ \\ = 1 + 25 \\ \\ = 26$

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Answer 2

Answer:

a^2 + b^2 = 26

a and b are zeros of the polynomial