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
If a, b, c, d ∈ R such that , then equation ax3 + bx2 + cx + d = 0 will have-...If the roots of the equation ax2 + bx + c = 0 are real and distinct, then -...If x1, x2, .........xn are any real numbers and n is any positive integer, then...If log0.3 (x - 1) 0.09 (x - 1), then x lies in the interval...The value of maximum real root minus the minimum real root of the equation $\left( x^{2} - 5 \right)^{4} + \left( x^{2} ...