Sum of roots of a quadratic equation is 17/6 and the product of the roots is -5/2 . Write the quadratic equation and solve it to find the roots

Question

pls give me the answer

Answer 1

x² + 17x/6 - 5/2 = 0 

Quadratic Formula or Complete the Square

x = (1/12)  [ -17  +/-  (649)^(1/2) ]

 

Answer 2

let x and y be the roots

x+y=17/6

xy=(-5/2)

y=17/6-x

substitute

x(17/6-x)=-5/2

x(17/6)-x^2=-5/2

multiply both sides by 6

17x-6x^2=-15

6x^2-17x-15=0

use the quadratic formula

[17±√(289+360)]/12

[17±√649]/12

649=11*59 and they are both prime, so nothing can be taken out of the radical

[17+√649]/12 and [17-√649]/12 are the roots

add them and multiply them to check:

add: (17+17)/12=34/12=17/6  (the 2 radicals cancel because they are opposites)

multiply: (17^2-649)/12=(289-649)/144=-360/144=-30/12=-5/2