Question

If α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2, then the value of

1. α²+β²
2. 1/α+1/β​

Can Someone Answer This Quick Thank You<3​

Answer 1

1. α²+β² = 25/36

2. 1/α+1/β​ = 1/2

Explanation:

Formula :

Consider the quadratic equation ax² + bx + c = 0

Where x₁ and x₂ are the zeros of the equation.

Then

`x_(1)+x_(2)=-(b)/(a) \\x_(1)* x_(2)=(c)/(a)`

……………………………………

α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2

Then

`\alpha +\beta =-(1)/(6)`

`\alpha * \beta =-(1)/(3)`

……………………

`\alpha^(2) +\beta^(2) =\left( \alpha +\beta \right)^(2) -2\alpha \beta`

`=\alpha^(2) +\beta^(2) =\left( -(1)/(6) \right)^(2) -2*(-(1)/(3) )`

`=(25)/(36)`

………………………………

`(1)/(\alpha ) +(1)/(\beta ) =(\alpha +\beta )/(\alpha \beta )`

`=(-(1)/(6) )/(-(1)/(3) ) =(1)/(2)`