Question

If the sum and product

of roots of a quadratic
equation are -7/2 and
5/2 respectively,then
the equation is :​

Answer 1

The equation is y = 2x² + 7x + 5

Explanation:

In the quadratic equation y = ax² + bx + c

• The roots of it are the values of x at y = 0

• The sum of the two roots =
  `(-b)/(a)`

• The product of the two roots =
  `(c)/(a)`

∵ The sum of the roots is
`(-7)/(2)`

∵ The product of the roots is
`(5)/(2)`

→ By using the rules above

∴
`(-b)/(a)` =
`(-7)/(2)`

∴
`(c)/(a)` =
`(5)/(2)`

→ Compare between them

∴ a = 2

∴ -b = -7 ⇒ divide both sides by -1

∴ b = 7

∴ c = 5

∵ The form of the quadratic function is y = ax² + bx + c

→ Substitute the values of a, b, and c in it

∴ y = 2x² + 7x + 5

∴ The equation is y = 2x² + 7x + 5