Advertisements
Advertisements
प्रश्न
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
Advertisements
उत्तर
Given: (x + a) is a factor of `2x^2 + 2ax + 5x + 10`
So, we have
x + a = 0
⇒ x = –a
Now, it will satisfy the above polynomial.
Therefore, we will get
`2 (–a)^2 + 2a(–a) + 5(–a) + 10 = 0`
`⇒ 2a^2 –2a^2 – 5a + 10 = 0`
`⇒ – 5a = – 10`
`⇒ a = 2`
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`
If α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
