Advertisements
Advertisements
प्रश्न
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
Advertisements
उत्तर
Let p(x) = x4 - a2x2 + 3x - a
Put x = -a in equation (i) we get
P(-a) = (-a)4 - a2 (-a)2 + 3(-a) -a
= a4 - a2 x a2 - 3a - a = -4a
But p(-a) = 0
⇒ -4a = 0
⇒ a = `(0)/(-4)`
⇒ a = 0.
संबंधित प्रश्न
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x3 + 2ax2 + ax - 1
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
f 2x3 + ax2 – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
