Question
Rational roots of the equation 2 x^4+x^3-11 x^2+ x+2=0 are
BITSAT
Mathematics
Quadratic Equation
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 1 2 and 2
- B. 1 2 , 2, 1 4 ,-2
- C. 1 2 , 2,3,4
- D. 1 2 , 2, 3 4 ,-2
Answer
A. 1 2 and 2
Step-by-step solution
Given equation can be reduced to a quadratic equation. 2 x^2+x-11+ 1 x + 2 x^2 =0 2 (x^2+ 1 x^2 )+ (x+ 1 x )-11=0 Put x+ 1 x =y 2 (y^2-2 )+y-11=0 2 y^2+y-15=0 y=-3 and 5 2 x+ 1 x =-3, x+ 1 x = 5 2 x^2+3 x+1=0,2 x^2-5 x+2=0 Only 2nd equation has rational roots as D =9 and roots are 1 2 and 2 .
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