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).`
APPEARS IN
संबंधित प्रश्न
Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.
`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`
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 are the zeros of the quadratic polynomial f(x) = 𝑥2 − 𝑥 − 4, find the value of `1/alpha+1/beta-alphabeta`
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are α + 2, β + 2.
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 quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
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.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
The number of polynomials having zeroes as –2 and 5 is ______.
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
3x2 + 4x – 4
Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
