Advertisements
Advertisements
प्रश्न
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
पर्याय
x2 − 9
x2 + 9
x2 + 3
x2 − 3
Advertisements
उत्तर
Since `alpha ` and `beta` are the zeros of the quadratic polynomials such that
`0 = alpha + beta`
If one of zero is 3 then
`alpha + beta =0`
`3 + beta = 0`
`beta = 0 -3`
`beta =-3`
Substituting `beta =-3` in `alpha + beta =0` we get
`alpha -3 =0`
`alpha =3`
Let S and P denote the sum and product of the zeros of the polynomial respectively then
`S = alpha+ beta`
`S = 0`
`P = alphabeta`
`P = 3xx-3`
` P = -9`
Hence, the required polynomials is
`= (x^2 - Sx + p)`
`= (x ^2 - 0x- 9)`
`= x^2 - 9`
Hence, the correct choice is `(a).`
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`f(x)=x^2-(sqrt3+1)x+sqrt3`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x − 2, find the value of `alpha/beta+beta/alpha`.
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` 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 the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
If 3 and –3 are two zeroes of the polynomial `(x^4 + x^3 – 11x^2 – 9x + 18)`, find all the zeroes of the given polynomial.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
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 number of polynomials having zeroes as –2 and 5 is ______.
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`
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
Find a quadratic polynomial whose zeroes are 6 and – 3.
Find the zeroes of the polynomial x2 + 4x – 12.
