Advertisements
Advertisements
प्रश्न
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
Advertisements
उत्तर
Let polynomial
P(x) = 3x3 + x2 – ax – 81
x – a is a factor of P(x)
Then putting x – a = 0
i.e. x = a in P(x) we get
P(a) = 0
3a3 + a2 – a × a – 81 = 0
3a3 = 81
a3 = 27
`\implies` a = (27)1/3 = 3
APPEARS IN
संबंधित प्रश्न
Show that 3x + 2 is a factor of 3x2 – x – 2.
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
If (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
