Advertisements
Advertisements
Question
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
Advertisements
Solution
Let `f(x) = 5x^3 - 7x^2 - ax - 28` be the given polynomial.
By the factor theorem,
(x − 4) is a factor of f(x).
Therefore f(4) = 0
Hence , `f(4) = 5(4)^2 - 7(4)^2 - a (4) - 28 = 0`
\[\Rightarrow 320 - 112 - 4a - 28 = 0\]
\[ \Rightarrow 180 - 4a = 0\]
\[ \Rightarrow a = \frac{180}{4} = 45\]
Hence, a = 45
APPEARS IN
RELATED QUESTIONS
Identify polynomials in the following:
`g(x)=2x^3-3x^2+sqrtx-1`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
x3 + 2x2 − x − 2
Factorize of the following polynomials:
x3 + 13x2 + 31x − 45 given that x + 9 is a factor
Let f(x) be a polynomial such that \[f\left( - \frac{1}{2} \right)\] = 0, then a factor of f(x) is
Factorise the following:
a2 + 10a – 600
Factorise the following:
12x2 + 36x2y + 27y2x2
Factorise the following:
(a + b)2 + 9(a + b) + 18
