Advertisements
Advertisements
प्रश्न
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
पर्याय
-1
1
-9
9
Advertisements
उत्तर
Let `alpha = 3` and `beta = -3` be the given zeros and y be the third zero of the polynomial `x^3 + x^2 -9x-9` then
Bt using `alpha + beta + y = (-text{coefficient of }x^2)/(text{coefficient of } x^3)`
`alpha + beta + y = -1/1`
`alpha + beta + y = -1`
Substituting `alpha = 3` and `beta =-3` in `alpha + beta + y = -1`, we get
` 3 - 3 + y =-1`
`y = -1`
Hence, the correct choice is `(a).`
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
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.
6x2 – 3 – 7x
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 p(s) = 3s2 − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`
Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, –1 and –3 respectively.
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 whose zeroes are `2/3` and `(-1)/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
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 2, –3 and 4.
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 two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.
The zeroes of the quadratic polynomial `4sqrt3"x"^2 + 5"x" - 2sqrt3` are:
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
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`
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
For the cubic equation \[ ax^{3} + bx^{2} + cx + d = 0 \] with roots \[ \alpha, \beta, \gamma \], the pairwise product \( \alpha\beta + \beta\gamma + \gamma\alpha \) equals:
