Advertisements
Advertisements
Question
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Advertisements
Solution
Let f(x) = x2 + ax + b
Since, (x – 2) is a factor of f(x).
∴ Remainder = f(2) = 0
(2)2 + a(2) + b = 0
4 + 2a + b = 0
2a + b = – 4 ...(i)
It is given that:
a + b = 1 ...(ii)
Subtracting (ii) from (i), we get,
a = –5
Substituting the value of a in (ii), we get,
b = 1 – (–5) = 6
APPEARS IN
RELATED QUESTIONS
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Show that x – 2 is a factor of 5x2 + 15x – 50.
Show that 3x + 2 is a factor of 3x2 – x – 2.
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
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 – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.
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.
