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
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
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.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
If mx2 – nx + 8 has x – 2 as a factor, then ______.
