Advertisements
Advertisements
प्रश्न
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
Advertisements
उत्तर
p(x) = ax2 + 5x + b
when (x − 2) is a factor
P(2) = 0
a(2)2 + 5(2) + b = 0
4a + 10 + b = 0
4a + b = −10 ...(1)
when `(x - 1/2)` is a factor
`"p"(1/2)` = 0
`"a"(1/2)^2 + 5(1/2) + "b"` = 0
Multiply by 4
a + 10 + 4b = 0
a + 46 = −10 ...(2)
From (1) and (2) we get
4a + b = a + 4b
4a – a = 4b – b
3a = 3b
a = b
Hence it is proved.
APPEARS IN
संबंधित प्रश्न
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Show that 3x + 2 is a factor of 3x2 – x – 2.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = x3 − x2 − x − 1, q(x) = x − 1
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.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
