Question

find the quadratic polynomial whoseroots are 5÷2and (–1÷4)​

Answer 1

given-

α=5/2 =2.5

β=-1/4 = -0.25

α+β= -b/a = 2.5-0.25=2.75

αβ=c/a = 0.625

hence the equation is -

x²-(α+β)x+(αβ)=0

x²-2.75x+0.625=0

hope this helps you.

Answer 2

Answer:

Step-by-step explanation:

let S be the sum of the roots and P the Product of the roots. then the quadratic equation is x^2 - Sx + P = 0.

S = 5 / 2 - 1 / 4 = 9 / 4

and

P = (5 / 2)×(- 1 / 4) = - 5 / 8

the quadratic equation is

x^2 - (9 / 4) x - 5 / 8 = 0

that is

8x^2 - 18 x - 5 = 0

and the quadratic polynomial is

8x^2 - 18 x - 5