Advertisements
Advertisements
प्रश्न
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Advertisements
उत्तर
Let 2x + 1 = 0, then x = `-(1)/(2)`
Substituting the value of x in f(x),
f(x) = 6x3 + 5x2 + ax – 2
`f(-1/2) = 6(-1/2)^3 + 5(-1/2)^2 + a(-1/2) - 2`
= `6(-1/8) + 5(1/4) + a(-1/2) - 2`
= `-(3)/(4) + (5)/(4) - a/(2) - 2`
= `(-3 + 5 - 2a - 8)/(4)`
= `(-6 - 2a)/(4)`
∴ 2x + 1 is a factor of f(x)
∴ Remainder = 0
∴ `(-6 - 2a)/(4)` = 0
⇒ –6 – 2a = 0
⇒ 2a = –6
⇒ a = –3
APPEARS IN
संबंधित प्रश्न
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Use factor theorem to factorise the following polynominals completely.
x3 + 2x2 – 5x – 6
If (x + 2) and (x – 3) are factors of x3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
