Advertisements
Advertisements
प्रश्न
Find the zeroes of the polynomial f(x) = `2sqrt(3)x^2 - 5x + sqrt(3)` and verify the relation between its zeroes and coefficients.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
`2sqrt(3)x^2 - 5x + sqrt(3)`
Advertisements
उत्तर
`2sqrt(3)x^2 - 5x + sqrt(3)`
⇒ `2sqrt(3)x^2 - 2x - 3x + sqrt(3)`
⇒ `2x(sqrt(3)x - 1) - sqrt(3)(sqrt(3)x - 1) = 0`
⇒ `(sqrt(3)x - 1) = 0` or `(2x - sqrt(3)) = 0`
⇒ `x = 1/sqrt(3)` or `x = sqrt(3)/2`
⇒ `x = 1/sqrt(3) xx sqrt(3)/sqrt(3)` = `sqrt(3)/3` or `x = sqrt(3)/2`
Sum of zeroes = `sqrt(3)/3 + sqrt(3)/2`
= `(5sqrt(3))/6`
= `(-("Coefficient of" x))/(("Coefficient of" x^2))`
Product of zeroes = `sqrt(3)/3 xx sqrt(3)/2`
= `sqrt(3)/6`
= `("Constant term")/(("Coefficient of "x^2))`
APPEARS IN
संबंधित प्रश्न
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.
`sqrt2 , 1/3`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
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)`
Find the zeroes of the quadratic polynomial 2x2 – 11x + 15 and verify the relation between the zeroes and the coefficients.
Find the quotient and the remainder when f(x) = x4 – 3x2 + 4x + 5 is divided by g(x) = x2 – x + 1.
On dividing 3x3 + x2 + 2x + 5 is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
The number of polynomials having zeroes as –2 and 5 is ______.
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
3x2 + 4x – 4
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`4x^2 + 5sqrt(2)x - 3`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
