Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
Advertisements
उत्तर
Let `f(x) = x^4 - a^2x^2 + 3x - a ` be the polynomial. By factor theorem, (x + a) is a factor of the f(x), if f(− a) = 0, i.e.,
`f(-a) = (-a)^4 - a^2 (-a)^2 + 3(-a)-a = 0`
`a^4 - a^4 - 3a - a = 0`
-4a = 0
`a = 0`
Thus, the value of a is 0.
APPEARS IN
संबंधित प्रश्न
Write the degrees of the following polynomials:
`12-x+2x^3`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3
f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 − 3x + 2
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
If (3x − 1)7 = a7x7 + a6x6 + a5x5 +...+ a1x + a0, then a7 + a5 + ...+a1 + a0 =
Factorise the following:
9 – 18x + 8x2
