Advertisements
Advertisements
प्रश्न
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
पर्याय
3
-3
5
-5
Advertisements
उत्तर
Let `alpha =sqrt5 ` and `beta -sqrt5` be the given zeros and y be the third zero of the polynomial `x^3 + 3x^2 - 5x -15`. Then,
By using `alpha + beta + y (-text{coefficient of }x^2)/(text{coefficient of } x^3)`
`alpha + beta + y = -3 /1`
`alpha + beta + y = -3`
Substituting `alpha = sqrt5` and `beta = -sqrt5` in `alpha + beta + y = -3`
We get
`sqrt5 - sqrt5 + y = -3`
`cancel(sqrt5) - cancel(sqrt5) + y = -3`
` y =-3`
Hence, the correct choice is `(b).`
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.
6x2 – 3 – 7x
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
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`.
If the zeros of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 – 3abc + a2d = 0.
Find the quadratic polynomial, the sum of whose zeroes is `(5/2)` and their product is 1. Hence, find the zeros of the polynomial.
Find a cubic polynomial whose zeroes are `1/2`, 1 and –3.
Define a polynomial with real coefficients.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
The zeroes of the polynomial r(t) = -12t2 + (k - 3)t + 48 are negative of each other. Then 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.
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
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`
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
For the quadratic equation \[ ax^{2} + bx + c = 0 \] with roots \[ \alpha, \beta \], which expression gives the product of the roots \( \alpha\beta \)?
