Question
Solve the cubic equation,
x³ − 7x² + 14x − 8 = 0 and Find all real roots.Solution
ATQ,
We first try to find at least one rational root. By Rational Root Theorem, possible rational roots are factors of 8: ±1, ±2, ±4, ±8 Test x = 1: 1³ − 7(1²) + 14(1) − 8 = 1 − 7 + 14 − 8 = 0 ✅ So (x − 1) is a factor. Now divide the cubic by (x − 1) using synthetic division: Coefficients: 1, −7, 14, −8 Bring down 1 Multiply 1×1 = 1, add to −7 → −6 Multiply 1×(−6) = −6, add to 14 → 8 Multiply 1×8 = 8, add to −8 → 0 So the cubic becomes: (x − 1)(x² − 6x + 8) = 0 Now solve the quadratic: x² − 6x + 8 = 0 Factor: (x − 2)(x − 4) = 0 So the full factorization is: (x − 1)(x − 2)(x − 4) = 0 Therefore, x = 1, 2, 4
Statements:Â Â Â Â Â
No book is a pencil.
All books are boards.
All boards are dusters.
No eraser is a duster.
...
Statements:All circles are rectangles.
No rectangle is a square.
Conclusions:I. No square is a rectangle.
II. Some rectangles are...
Statements : Some eggs are chickens.
No chicken is a hen.
No hen is a pigeon.
Conclusions : I. Some eggs may be hens.
II....
Statements :
All sparrows are parrots.
No parrot is bird.
All birds are peacocks.
Conclusions:
I. Some birds are ...
Statements: Some cars are scooters.
      All scooters are bikes.
Conclusions: I. some cars are bikes.
   II. Some...
Statements:Some students are Rich.
No Rich is a teacher.
Conclusions:I. Some teacher are not Rich.
II. Some Rich are students.
Statements: All flowers are books.
All books are carpets.
Some carpets are keys.
Some keys are locks.
Conclusions:I. Some ke...
Statement:
At-least some chairs are tables.
A few tables are fans.
Only a few windows are tables.
All tables are doors.
Statement:Â
Some jeans are not shirt.
All shirts are pant.
Some pants are not blazers.
Conclusion:
I. Some blaze...
Statements:
Only a few passage is comprehension
A few comprehension is language
All language is story
Conclusions: ...
