Advertisements
Advertisements
प्रश्न
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
पर्याय
a + c + e = b + d
a + b +e = c + d
a + b + c = d + e
b + c + d = a + e
Advertisements
उत्तर
As`(x^2 - 1)`is a factor of polynomial
f(x2) = ax4 + bx3 + cx2 + dx + e
Therefore,
f(x) = 0
And
f(1) = 0
\[a \left( 1 \right)^4 + b \left( 1 \right)^3 + c \left( 1 \right)^2 + d\left( 1 \right) + e = 0\]
\[ \Rightarrow a + b + c + d + e = 0\]
And
f(-1) = 0
`a(-1)^4 + b(-1)^3 +c(-1)^2 + d(-1) + e = 0`
`a - b + c - d + e = 0`
Hence, a+c+e = b+d.
APPEARS IN
संबंधित प्रश्न
Identify polynomials in the following:
`h(x)=x^4-x^(3/2)+x-1`
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
f(x) = x3 −6x2 − 19x + 84, g(x) = x − 7
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
x3 − 23x2 + 142x − 120
y3 − 7y + 6
x4 + 10x3 + 35x2 + 50x + 24
Factorise the following:
6x2 + 16xy + 8y2
