Advertisements
Advertisements
प्रश्न
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
Advertisements
उत्तर
Let `f(x) = x^3 - 2ax^2 + ax - 1` be the given polynomial.
By factor theorem, if (x − 2) is a factor of f(x), then f (2) = 0
Therefore,
`f(2) = (2)^3 - 2a(2)^2 a(2) - 1 = 0`
`8-8a + 2a - 1 = 0`
`-6a + 7 = 0`
`a = 7/6`
Thus the value of a is 7/6.
APPEARS IN
संबंधित प्रश्न
Write the coefficient of x2 in the following:
`sqrt3x-7`
Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
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) = x3 −6x2 − 19x + 84, g(x) = x − 7
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
y3 − 2y2 − 29y − 42
The value of k for which x − 1 is a factor of 4x3 + 3x2 − 4x + k, is
Factorise the following:
5x2 – 29xy – 42y2
