Question

The sum and product of two roots of an equation is 4 and -5/2 their quadratic equation is​

Answer 1

x2 - ( sum of zeros )x + ( product of zeros)

x2 - (4)X + ( -5/2 )

2x2 -8x - 5

Answer 2

Answer:

The quadratic Equation = x² - 4x - 5/2 = 0

On Simplifying, The quadratic Equation =

$\boxed{\sf \bold 2x^2 - 8x - 5 = 0}$

SOLUTION

Let us Assume that α and β are the two roots(zeros) of the quadratic polynomial.

Given

The Sum of two roots of the equation = 4

$\implies$

α + β = 4

Also,given that product of two roots = - 5/2

$\implies$

αβ = - 5/2

General Form of a Quadratic Polynomial

$\boxed {\sf x^2 - (\alpha + \beta )x + \alpha \beta }} \longrightarrow(1)$

Substituting the given values in (1) ,

α + β = 4

  and

αβ = - 5/2

x² - 4x - 5/2 =0

On Taking LCM and Solving,

{LCM = 2}

The Quadratic Equation is:-

$\boxed{\sf 2x^2 - 8x - 5 = 0}$