Question

The relationship between the zeroes and coefficient of the quadratic polynomial ax^2+bx+c is a: alpha •beta =c/a , b: alpha •beta =-b/a c: alpha •beta -c/ a , d: alpha •beta =b/a ( please give full explanation of answer !!!​

Answer 1

I hope this what you wanted

Answer 2

The relationship between the zeroes and coefficient of the quadratic polynomial is ax² + bx + c is ..

1. αβ = c/a
2. αβ = -b/a
3. αβ = -c/a
4. αβ = b/a

here quadratic polynomial is ax² + bx + c.

let α and β are zeroes of the given polynomial.it means, (x - α) and (x - β) are factors of the polynomial.

i.e., ax² + bx + c = a(x - α)(x - β)

⇒ax² + bx + c = a[x² - βx - αx + αβ]

⇒ax² + bx + c = ax² - a(α + β)x + aαβ

now comparing with both polynomials,

we get,

b = -a(α + β) ⇒(α + β) = -b/a

and c = aαβ ⇒αβ = c/a

hence option (1) αβ = c/a , is correct choice.