Q. 65.0( 1 Vote )
What first degree polynomial added to 2x3 – 3x2 + 5x + 1 gives a multiple of x2 – 1?
Answer :
Given, 2x3 – 3x2 + 5x + 1
Need to find the first degree polynomial if added to the equation gets the multiple of x2 – 1
⇒ 2x3 – 3x2 + 5x + 1 can be written as 2(x3 – 
x2 + 
x + 
)
⇒ x3 – 
x2 + 
x + 
= (x2 – 1)(x – a) + b
= x3 – ax2 – x + a + b
∴ a = 
and a + b = 
⇒ b = – 1
Rate this question :
Champ Quiz |Revealing the relation Between Zero and Coefficients38 mins
Relation Between zeroes and Coefficients46 mins
Interactive Quiz:Polynomials43 mins
Division Algorithm-130 mins
Relation b/w The Zeroes and Coefficients of Cubic Polynomials54 mins
Solving Imp. Qs. of Olympiad on Polynomials47 mins
Revision of Relation Between the Zeroes and Coefficients of Quadratic Polynomial46 mins
Interactive Quiz - Geometrical Meaning of the Zeroes32 mins
Relationship between Zeroes and Coefficients-238 mins
Cubic Polynomial36 mins
In each pair of polynomials below find what kind of natural number n must be, so that the first is a factor of the second.
x2 – 1, xn – 1
Kerala Board Mathematics Part-2In each pair of polynomials below find what kind of natural number n must be, so that the first is a factor of the second.
x – 1, xn + 1
Kerala Board Mathematics Part-2What first degree polynomial added to 2x3 – 3x2 + 5x + 1 gives a multiple of x2 – 1?
Kerala Board Mathematics Part-2In each pair of polynomials below find what kind of natural number n must be, so that the first is a factor of the second.
x + 1, xn – 1
Kerala Board Mathematics Part-2In each pair of polynomials below find what kind of natural number n must be, so that the first is a factor of the second.
x – 1, xn – 1
Kerala Board Mathematics Part-2Prove that if x2 – 1 is a factor of ax3 + bx3 + cx + d, then a = –c and b = –d.
Kerala Board Mathematics Part-2In each pair of polynomials below find what kind of natural number n must be, so that the first is a factor of the second.
x + 1, xn + 1
Kerala Board Mathematics Part-2For each pair of polynomials below, find the quotient and remainder on dividing the first by the second.
x3 + 1, x + 1
Kerala Board Mathematics Part-2For each pair of polynomial is below, check whether the first is a factor of the second. If not a factor, find the remainder on dividing the second by the first.
2x – 1, 3x3 – x2 – 8x + 6
Kerala Board Mathematics Part-2For each pair of polynomials below, find the quotient and remainder on dividing the first by the second.
x3 – 1, x – 1
Kerala Board Mathematics Part-2