Quadratic EquationHard
Question
If α ≠ β but α2 = 5α - 3 and β3 = 5β - 3 then the equation having α/β and β/α as its roots is
Options
A.3x2 - 19 x + 3 = 0
B.3x2 + 19 x - 3 = 0
C.3x2 - 19 x - 3 = 0
D.x2 - 5x + 3 = 0
Solution
We have α2 = 5α - 3
⇒ α2 - 5α + 3 = 0 ⇒ α =
. Similarly, β2 = 5β - 3 ⇒ α =
∴ α =
and β = 
or vice - versa
α2 + β2 =
= 19 & αβ = 
(25 - 13)= 3
Thus, the equation having
as its roots is
x2 - x
+ 
= 0 ⇒ x2 - x 
+ 1 = 0 or 3x2 - 19x + 1 = 0
⇒ α2 - 5α + 3 = 0 ⇒ α =
. Similarly, β2 = 5β - 3 ⇒ α = ∴ α =
and β = or vice - versaα2 + β2 =
= 19 & αβ = (25 - 13)= 3 Thus, the equation having
as its roots is x2 - x
+ = 0 ⇒ x2 - x + 1 = 0 or 3x2 - 19x + 1 = 0Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
The possible values of ' $b$ ', $b \in R$ for which the equations $2017x^{2} + bx + 7102 = 0$ and $7102x^{2} + bx + 2017...If α and β are the roots of the equation x2 - x + 1 = 0, then α2009 + β2009 =...If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx +...Let (x0, y0) be solution of the following equations (2x)ln2 = (3y)ln3 3lnx = 2lny Then x0 is...If one root of the equation x2 − x − k = 0 is square of the other, then k equals to -...