Advertisements
Advertisements
प्रश्न
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`y^2 + 3/2 sqrt(5)y - 5`
Advertisements
उत्तर
Let p(y) = `y^2 + 3/2 sqrt(5)y - 5`
= `2y^2 + 3sqrt(5)y - 10`
= `2y^2 + 4sqrt(5)y - sqrt(5)y - 10`
= `(y + 2sqrt(5))(2y - sqrt(5))`
So, the zeroes of p(y) are `-2sqrt(5)` and `sqrt(5)/2`
∴ Sum of zeroes = `-2sqrt(5) + sqrt(5)/2`
= `(-3sqrt(5))/2`
= `(-("coefficient of" y))/("coefficient of" y^2)`
And product of zeroes = `-2sqrt(5) xx sqrt(5)/2` = –5
= `"constant term"/("coefficient of" y^2)`
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 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 a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(2beta)/alpha`
If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
The product of the zeros of x3 + 4x2 + x − 6 is
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial 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:
4x2 – 3x – 1
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
5t2 + 12t + 7
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2x^2 + (7/2)x + 3/4`
Find the zeroes of the polynomial x2 + 4x – 12.
