Advertisements
Advertisements
प्रश्न
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
विकल्प
-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).`
APPEARS IN
संबंधित प्रश्न
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
`g(x)=a(x^2+1)-x(a^2+1)`
If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`.
If the zeros of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 − 3abc + a2d = 0.
If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
If 1 and –2 are two zeroes of the polynomial `(x^3 – 4x^2 – 7x + 10)`, find its third zero.
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.
Define a polynomial with real coefficients.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
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.
`(-8)/3, 4/3`
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.
`21/8, 5/16`
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
Find the zeroes of the polynomial x2 + 4x – 12.
