Question

Form a quadratic equation whose roots are -3 and -6​

Answer 1

Solution:

Given That: Roots of the equation are -3 and -6.

We know that, If α and β are the roots of a quadratic equation, then the equation will be:

→ x² - (α + β)x + αβ = 0

Here, -3 and -6 are the roots of the equation. So, our equation will be:

→ x² - (-3 - 6)x + (-3) × (-6) = 0

→ x² + 9x + 18 = 0

★ Which is our required answer.

Answer:

• The required quadratic equation is x² + 9x + 18 = 0

To Know More:

Proof of x² - (α + β)x + αβ = 0

Let α and β be the roots of a quadratic equation in terms of x.

So, we can say that:

→ x = α

→ x = β

We can also write:

→ (x - α) = 0

→ (x - β) = 0

α and β are the roots so (x - α) and (x - β) will be the factor.

So, the equation will be:

→ (x - α)(x - β) = 0

→ x(x - β) - α(x - β) = 0

→ x² - βx - αx + αβ = 0

→ x² - (α + β)x + αβ = 0