Advertisements
Advertisements
प्रश्न
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
Advertisements
उत्तर
f(x) = ax2 + bx + c
α + β = `(-b/a)`
αβ = `c/a`
since α + β are the roots (or) zeroes of the given polynomials
then
α - β
The two zeroes of the polynomials are
`(-b+sqrt(b^2-4ac))/(2a)-((-b-sqrt(b^2-4ac))/(2a))=(-b+(sqrt(b^2-4ac)+b+sqrt(b^2-4ac)))/(2a)=(2sqrt(b^2-4ac))/(2a)=(sqrt(b^2-4ac))/a`
संबंधित प्रश्न
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
g(x) = a(x2 + 1) – x(a2 + 1)
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
If the squared difference of the zeros of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, find the value of p.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – 1, find a quadratic polynomial whose zeros are `(2alpha)/beta` and `(2beta)/alpha`.
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
Find the zeroes of the quadratic polynomial (3x2 – x – 4) and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial whose zeroes are `2/3` and `(-1)/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are `1/2`, 1 and –3.
If 1 and –2 are two zeroes of the polynomial (x3 – 4x2 – 7x + 10), find its third zero.
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
The product of the zeros of x3 + 4x2 + x − 6 is
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 ______.
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
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)`
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.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
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?
A quadratic equation whose roots are \[ \alpha, \beta \] can be written as:
