Q. 24.1( 27 Votes )
If (x + 1) is a factor of polynomial f(x) = mx2 – x + 1. Find the value of m2.
Answer :
Given:
f(x) = mx2 – x + 1
(x + 1) is factor of f(x)
Concept Used:
The factor theorem states that a polynomial has a factor if and only if it is a root.
Or
If (x – a) is a factor of f(x), then f(a) = 0
Explanation:
x + 1 = 0
x = –1
f(–1) = m.(–1)2 + 1 + 1 = 0
m + 2 = 0
m = –2
m2 = (–2)2 = 4
Hence, m2 = 4
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
Interactive Quiz - Geometrical Meaning of the Zeroes32 mins
Relationship between Zeroes and Coefficients-238 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
Cubic Polynomial36 mins
Divide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :
p(x) = x3 – 3x2 + 4x + 2 , g(x) = x – 1
KC Sinha - MathematicsDivide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :
p(x) = x3 – 3x2– x + 3, g(x) = x2 – 4x + 3
KC Sinha - MathematicsWhen a polynomial p(x) is divided by (2x + 1), is it possible to have (x - 1) as a remainder? Justify your answer.
RS Aggarwal - MathematicsDivide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :
p(x) = x4 + 2x3 – 3x2 + x – 1, g(x) = x – 2
KC Sinha - MathematicsFind all the zeroes of the polynomial given below having given numbers as its zeroes.
x4 – 6x3 – 26x2 + 138x – 35;2±√3
KC Sinha - MathematicsDivide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :
p(x) = x6 + 3x2 + 10 and g(x) = x3 + 1
KC Sinha - MathematicsDivide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :
p(x) = x4 + 1, g(x) = x + 1
KC Sinha - MathematicsVerify that 
are the zeroes of the cubic polynomial p(x) = 3x2 – 5x2 – 11x – 3 and then verify the relationship between the zeroes and the coefficients.
Find all the zeros of the polynomial,
if two of its zeros are √3 and 
.
