Advertisements
Advertisements
प्रश्न
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Advertisements
उत्तर
Let p(x) = 2x3 + ax2 + bx - 14
Given, (x – 2) is a factor of p(x),
⇒ Remainder = p(2) = 0
⇒ 2(2)3 + a(2)2 + b(2) – 14 = 0
⇒ 16 + 4a + 2b – 14 = 0
⇒ 4a + 2b + 2 = 0
⇒ 2a + b + 1 = 0 ...(1)
Given, when p(x) is divided by (x – 3), it leaves a remainder 52
∴ p(3) = 52
∴ 2(3)3 + a(3)2 + b(3) – 14 = 52
⇒ 54 + 9a + 3b - 14 - 52 = 0
⇒ 9a + 3b – 12 = 0
⇒ 3a + b – 4 = 0 ...(2)
Subtracting (1) from (2), we get,
a – 5 = 0 ⇒ a = 5
From (1),
10 + b + 1 = 0 ⇒ b = –11
APPEARS IN
संबंधित प्रश्न
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; show that : `a = (n - q)/(m - p)`
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Find the value of a , if (x - a) is a factor of x3 - a2x + x + 2.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
If p(a) = 0 then (x – a) is a ___________ of p(x)
