Advertisements
Advertisements
प्रश्न
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
विकल्प
- \[\frac{- d}{a}\]
- \[\frac{c}{a}\]
- \[\frac{- b}{a}\]
- \[\frac{b}{a}\]
Advertisements
उत्तर
Let `alpha = 0, beta=0` and y be the zeros of the polynomial
f(x)= ax3 + bx2 + cx + d
Therefore
`alpha + ß + y= (-text{coefficient of }X^2)/(text{coefficient of } x^3)`
`= -(b/a)`
`alpha+beta+y = -b/a`
`0+0+y = -b/a`
`y = - b/a`
`\text{The value of} y - b/a`
Hence, the correct choice is `(c).`
APPEARS IN
संबंधित प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α2β + αβ2
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
If the squared difference of the zeros of the quadratic polynomial f(x) = x2 + px + 45 is equal to 144, find the value of p.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`.
Verify that 3, -2, 1 are the zeros of the cubic polynomial `p(x) = (x^3 – 2x2 – 5x + 6)` and verify the relation between it zeros and coefficients.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
Find all the zeroes of `(x^4 + x^3 – 23x^2 – 3x + 60)`, if it is given that two of its zeroes are `sqrt3 and –sqrt3`.
Define a polynomial with real coefficients.
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
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.
`(-3)/(2sqrt(5)), -1/2`
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
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`.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
