Advertisements
Advertisements
प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.
`sqrt2 , 1/3`
उत्तर
Given: α + β = `sqrt2`, αβ = `1/3`
Since ax2 + bx + c = kx2 - k(α + β)x + kαβ
or ax2 + bx + c = k[x2 - (α + β)x + αβ]
Or `(ax^2 + bx + c)/k = (x^2 - sqrt2x + 1/3)`
Or `(ax^2 + bx + c)/k = (3x^2 - 3sqrt2x + 1)/3`
Here k is a constant term, by comparing k = 3
Hence, ax2 + bx + c = `3x^2 - 3sqrt2x + 1`
The quadratic polynomial is `3x^2 - 3sqrt2x + 1`.
APPEARS IN
संबंधित प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
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 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(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
If α and β are the zeros of the quadratic polynomial p(s) = 3s2 − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are α + 2, β + 2.
Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`.
Find a cubic polynomial whose zeroes are 2, -3and 4.
If 1 and –2 are two zeroes of the polynomial `(x^3 – 4x^2 – 7x + 10)`, find its third zero.
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial is:
A quadratic polynomial, whose zeroes are –3 and 4, is ______.
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`(-3)/(2sqrt(5)), -1/2`
Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
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.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
