Question

find the quadratic equation in x whose roots are a+2 and b/4-1​

Answer 1

Answer:

We will learn the formation of the quadratic equation whose roots are given.

To form a quadratic equation, let α and β be the two roots.

Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).

According to the problem, roots of this equation are α and β.

Therefore,

α + β = - baba and αβ = caca.

Now, ax22 + bx + c = 0

⇒ x22 + babax + caca = 0 (Since, a ≠ 0)

 

⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]

⇒ x22 - (sum of the roots)x + product of the roots = 0

⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)

Formula (i) is used for the formation of a quadratic equation when its roots are given.

For example suppose we are to form the quadratic equation whose roots are 5 and (-2). By formula (i) we get the required equation as

x22 - [5 + (-2)]x + 5 ∙ (-2) = 0

⇒ x22 - [3]x + (-10) = 0

⇒ x22 - 3x - 10 =Hope it help