Question

the root of a quadratic equation are ( 1,3) (4,6) (1,7)(8,5)​

Answer 1

Answer:

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 = 0