Question

If α and β are the zeros of the polynomial f(x)=5x^2+4x−9 then evaluate the following: alpha^2+beta^2​

Answer 1

Answer:

Step-by-step explanation:

here,given α and β are zeros of given polynomial f(x)=5x²+4x-9

acording to question,

f(x)=0

5x²+4x-9=0

5x²-5x+9x-9=0

5x(x-1)+9(x-1)=0

(x-1)(5x+9)=0

so ,x=1 or -9/5

hence,α=1 and β= -9/5

now,α²+β²=1+(-9/5)²=1+81/25=106/25.

is the correct answer.

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