Question

A quadratic equation in the variable y whose roots are α and β is *
1.by² - y(α + β) - αβ = 0
2. y² - y(α + β) + αβ = 0
3. y² + y(α + β) - αβ = 0
4. y² + y(α + β) + αβ = 0
plsz answer fast I'll mark u as the brainliest​

Answer 1

Step-by-step explanation:

If s is the sum of roots and p is the product of roots of a quadratic equation, then the quadratic equation is:

y² - sy + p = 0

s = α+β

p = αβ

So,

f(y) = y² - (α+β)y + αβ = 0

Proof:

ay² + by + c = 0

Dividing throughout by a,

y² + (b/a)y + (c/a) = 0 -------(1)

We know that,

α+β = -b/a and αβ = c/a -------(2)

(2) in (1),

y² - (α+β)y + αβ = 0