Roots of quadratic equation

anpanman SG

The roots of the equation 4x^2 - x + 36 - 0 are alfa^2 and beta^2

find 2 distinct equations whose roots are alfa and beta. my tb 's answer is 2x^2 +(-) 5x +6 = 0 But I think the answer's wrong. Eh, you can just provide me the answer because I think I should be able to solve it myself. ;)

skythewood SG

i see the - 0 in the equation.

and i try to think why there is a 0 in the equation,

Music-Life SG

maybe he tried to type in = 0

jayh272416 SG

a^2+b^2 sum of roots is 1/4
a^2b^2 product of roots is 9

(a+b)^2 = a^2+b^2+2ab
ab = 3 or -3
(a+b)^2 = 6 1/4 or -5 3/4 (reject as it is less than 0)
a+b = sqrt (6 1/4) = 5/2 or -5/2

sum of roots is 5/2 or -5/2
product of roots is 3

therefore eqn is x^2-5/2x+3 = 0 or x^2+5/2x+3 = 0

so 2x^2-5x+6 = 0 or 2x^2+5x+6=0

so u are correct