Advertisements
Advertisements
प्रश्न
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
पर्याय
1
2
4
5
Advertisements
उत्तर
If `x = alpha`, is a zero of a polynomial then `x -alpha `is a factor of `f(x)`
Since 3 is the zero of the polynomial , f(x) = x2 − 5x + 4,
Therefore `x - 3`is a factor of `f(x)`
Now, we divide`f(x) = x^2 - 5x + 4 ` by `(x - 3)` we get
Therefore we should add 2 to the given polynomial
Hence, the correct choice is (b).
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha + b) + 1/(abeta + b)`.
If α and β are the zeros of the quadratic polynomial p(x) = 4x2 – 5x – 1, find the value of α2β + αβ2.
If the zeros of the polynomial f(x) = 2x3 – 15x2 + 37x – 30 are in A.P., find them.
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, –2 and –24 respectively.
Find the quotient and the remainder when f(x) = x4 – 5x + 6 is divided by g(x) = 2 – x2.
If α, β are the zeroes of the polynomial f(x) = x2 + x – 2, then `(α/β - α/β)`.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
The zeroes of the polynomial r(t) = -12t2 + (k - 3)t + 48 are negative of each other. Then k is ______.
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, then find the values of p and q.
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
Find a quadratic polynomial whose zeroes are 6 and – 3.
In the relation between zeroes (roots) and coefficients of \[ ax^{2} + bx + c = 0 \], what is the status of the pairwise product of the roots?
