Advertisements
Advertisements
Question
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
Options
- \[\frac{- d}{a}\]
- \[\frac{c}{a}\]
- \[\frac{- b}{a}\]
- \[\frac{b}{a}\]
Solution
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
RELATED QUESTIONS
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
Verify that 5, -2 and 13 are the zeroes of the cubic polynomial `p(x) = (3x^3 – 10x^2 – 27x + 10)` and verify the relation between its zeroes and coefficients.
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial 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.
`21/8, 5/16`
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
