मराठी

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.

पर्याय

  • `- c/a`

  • `c/a`

  • 0

  • `- b/a`

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is `underlinebb(c/a)`.

Explanation:

According to the question,

We have the polynomial,

ax3 + bx2 + cx + d

We know that,

Sum of product of roots of a cubic equation is given by `c/a`

It is given that one root = 0

Now, let the other roots be α, β

So, we get,

αβ + β(0) + (0)α = `c/a`

αβ = `c/a`

Hence the product of other two roots is `c/a`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Polynomials - Exercise 2.1 [पृष्ठ ९]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 10
पाठ 2 Polynomials
Exercise 2.1 | Q 5 | पृष्ठ ९

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.


if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify  the relation between zeros and its cofficients


Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

t2 – 15


Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 

`1/4 , -1`


If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.


Find the zeroes of the quadratic polynomial f(x) = 4x2 - 4x - 3 and verify the relation between its zeroes and coefficients.


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 𝛼, 𝛽 are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?` 


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 α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]


The product of the zeros of x3 + 4x2 + x − 6 is


The number of polynomials having zeroes as –2 and 5 is ______.


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


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`


Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`y^2 + 3/2 sqrt(5)y - 5`


Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.


Find the zeroes of the polynomial x2 + 4x – 12.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×