If alpha and beta are the zeroes of p(x) = 2x^2 - 5x +3. then find a quadratic polynomial whose zeroes are 1/alpha and 1/beta?

Question

Answer

Quadratic Polynomial with Zeroes 1/alpha and 1/beta:

To find a quadratic polynomial with zeroes 1/alpha and 1/beta, we need to understand the relationship between the zeroes of a quadratic polynomial and its coefficients. A quadratic polynomial is given in the form:

p(x) = ax^2 + bx + c

where 'a', 'b', and 'c' are the coefficients of the polynomial.

Relationship between Zeroes and Coefficients:

For a quadratic polynomial, the sum of the zeroes is equal to the negation of the coefficient of the linear term (b/a), and the product of the zeroes is equal to the constant term (c/a).

Let's consider the given quadratic polynomial:

p(x) = 2x^2 - 5x + 3

Here, the sum of the zeroes is equal to -(-5/2) = 5/2, and the product of the zeroes is equal to 3/2.

Finding the Zeroes:

We are given that alpha and beta are the zeroes of the polynomial p(x) = 2x^2 - 5x + 3.

Using the quadratic formula, we can find the zeroes:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values of 'a', 'b', and 'c' from the given polynomial, we have:

x = (-(-5) ± √((-5)^2 - 4(2)(3)))/(2(2))

x = (5 ± √(25 - 24))/(4)

x = (5 ± √(1))/(4)

x = (5 ± 1)/(4)

One zero is obtained when we take the positive square root:

x = (5 + 1)/(4) = 6/4 = 3/2

Another zero is obtained when we take the negative square root:

x = (5 - 1)/(4) = 4/4 = 1

Therefore, the zeroes of the polynomial p(x) = 2x^2 - 5x + 3 are 3/2 and 1.

Finding the Quadratic Polynomial with Zeroes 1/alpha and 1/beta:

Now, we want to find a quadratic polynomial with zeroes 1/alpha and 1/beta.

Let's consider a new quadratic polynomial:

q(x) = k(x - 1/alpha)(x - 1/beta)

Here, 'k' is a constant that can be any non-zero value.

The zeroes of the polynomial q(x) are

Similar Class 10 Doubts

If alpha and beta are the zeroes of the quadratic polynomial :p(x) =3x^2 - 4x 1, find a quadratic polynomial whose zeroes are alpha^2/beta and beta^2/alpha ?

If alpha and beta are zeroes of a quadratic polynomial Fx = 2x square -5x 7. Find a polynomial who's zeroes are 2 alpha 3 beta and 3 alpha 2 beta?

If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta?

if alpha and beta are the zeros of the polynomial f(x)=x^2-3x-2. find a quadratic polynomial whose zeroes are 1/2alpha +beta,1/2beta +alpha

if alpha and beta are the zeroes of the polynomial 21x²_x_2,find a quadratic polynomial who 's zeroes are 2alpha and 2beta Related: Ex 2.2 NCERT Solutions - Polynomials?

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Suggested Free Tests

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company