Question

If α and β are the zeroes of the quadratic polynomial
f(x) = 6x^2
+ x -2 then find the value of α ^2+β^2.​

Answer 1

f(x) = 6x² + x - 2

Now, let ɑ and β be the zeroes of f(x)

So, We know

☛ product of zeroes = (constant term) / (coefficient of x²)

==> ɑβ = -1/3 ...(1)

Also,

☛ sum of zeroes = -(coefficient of x) / (coefficient of x²)

==> ɑ + β = -1/6

Square both sides

==> (ɑ + β)² = 1/36

==> ɑ² + β² + 2ɑβ = 1/36

==> ɑ² + β² = 1/36 + 2/3 { from (1) }

==> ɑ² + β² = (1 + 24)/36

==> ɑ² + β² = 25/36