Advertisements
Advertisements
प्रश्न
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
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
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
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.
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
Factors of 3x3 – 2x2 – 8x are ______.
