Advertisements
Advertisements
प्रश्न
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
विकल्प
- \[- \frac{b}{d}\]
- \[\frac{c}{d}\]
- \[- \frac{c}{d}\]
- \[- \frac{c}{a}\]
Advertisements
उत्तर
We have to find the value of `1/alpha + a/beta+1/y`
Given `alpha , beta ,y` be the zeros of the polynomial f(x) = ax3 + bx2 + cx + d
We know that
`alpha ß + beta y + yalpha= - (text{coefficient of x})/(text{coefficient of } x^3)`
`= c/a`
`alphabetay= (-\text{Coefficient of x})/(\text{Coefficient of}x^3)`
`=(-d)/a`
So
`1/alpha + 1/beta+1/y=((c)/a)/(-d/a)`
`1/alpha + 1/beta + 1/y = c/axx(-a/d)`
`1/alpha+ 1/beta+1/y =-c/d`
Hence, the correct choice is `(c)`.
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
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 `1/alpha+1/beta-2alphabeta`
If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
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.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
If 𝛼, 𝛽 are the zeroes of the polynomial f(x) = x2 + x – 2, then `(∝/β-∝/β)`
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then 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:
`4x^2 + 5sqrt(2)x - 3`
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.
`-2sqrt(3), -9`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`7y^2 - 11/3 y - 2/3`
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
