Advertisements
Advertisements
प्रश्न
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Advertisements
उत्तर
`2sqrt3x^2-5x+sqrt3`
`2sqrt3x^2-2x-3x+sqrt3`
`2x(sqrt3x-1) or (2x-sqrt3=)=0`
`(sqrt3x-1)=0 or (2x-sqrt3)=0`
`x=1/sqrt3 or x=sqrt3/2`
`x=1/sqrt3xxsqrt3/sqrt3=sqrt3/3 or x=sqrt3/2`
Sum of zeroes= `sqrt3/3+sqrt2=(5sqrt3)/6 = -(("coefficient of" x))/(("coefficient of" x^2))`
Product of zeroes=`sqrt3/3xxsqrt3/2=sqrt3/6= ("constant term")/(("coefficient of "x^2))`
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.
if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify the relation between zeros and its cofficients
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
1, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α2β + αβ2
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :
`a(α^2/β+β^2/α)+b(α/β+β/α)`
If α and β are the zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of `1/alpha+1/beta`
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
Verify that 5, -2 and 13 are the zeroes of the cubic polynomial `p(x) = (3x^3 – 10x^2 – 27x + 10)` and verify the relation between its zeroes and coefficients.
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
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.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
Find a quadratic polynomial whose zeroes are 6 and – 3.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
