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 constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x .
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
2x4 − 7x3 − 13x2 + 63x − 45
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
If x + 2 is a factor of x2 + mx + 14, then m =
Factorise the following:
`1/x^2 + 1/y^2 + 2/(xy)`
Factorise:
3x3 – x2 – 3x + 1
