Let alpha and beta are the zeroes of quadratic polynomial 2x^2-5x-6 then form a quadratic polynomial whose zeroes are alpha + beta and alpha×beta?

Question

Answer

P(x)=2x²-5x-6,having zeros as alpha and beta,
to find -->f(x) such that its zeros are (alpha +beta)and alpha×beta,
in p(x) sum of zeros=alpha+beta=-b/a,
alpha+beta=-(-5)/2=5/2,
product of zeros=alpha×beta=c/a,
alpha×beta=-6/2=-3,
zeros of f(x) are 5/2 and -3,
f(x)=x²-( sum of zeros)x+ product of zeros,
=x²-(5/2-3)x+(5/2×-3),
=x²-(-1/2)x-(15/2),
=x²+1/2x-15/2,
=2x²+x-15

Answer

Answer

Since alpha and beta are the zeroes of the polynomial 2x^2 -5x -6 therefore alpha + beta = -b/a = -(-5)/2 = 5/2and alpha x beta = c/a = -6/2 = -3
since alpha + beta and alpha x beta are zeroes of another polynomial
therefore sum of zeroes = 5/2 + (-3) = -1/2product of zeroes = 5/2 x (-3) = -15/2
therefore the polynomial would be:
x^2 - (sum of zeroes)x + product of zeroes= x^2 + 1/2x -15/2= 2x^2 + x - 15
therefore the required polynomial is 2x^2 + x -15

Answer

How to Form a Quadratic Polynomial with Given Zeroes

Given Information:

Quadratic polynomial: 2x^2-5x-6

Zeroes: alpha and beta

Finding the Value of Alpha and Beta

Using the quadratic formula, we can find the values of alpha and beta:

x = (-b ± √(b^2-4ac))/2a

For the given quadratic polynomial, a = 2, b = -5, and c = -6

Substituting these values in the quadratic formula, we get:

alpha = (-(-5) + √((-5)^2-4(2)(-6)))/2(2) = 3

beta = (-(-5) - √((-5)^2-4(2)(-6)))/2(2) = -1.5

Finding the Value of Alpha×Beta

Using the product of roots formula, we can find the value of alpha×beta:

alpha×beta = c/a = -6/2 = -3

Forming the Quadratic Polynomial

Let the quadratic polynomial with zeroes alpha, beta, and alpha×beta be ax^2 + bx + c

We know that:

alpha + beta = b/a

alpha×beta = c/a

Substituting the values of alpha, beta, and alpha×beta, we get:

3 + (-1.5) + (-3) = b/2

b = -1

-3 = c/2

c = -6

Therefore, the quadratic polynomial with zeroes alpha, beta, and alpha×beta is:

2x^2 - x - 6

Final Answer:

The quadratic polynomial with zeroes alpha, beta, and alpha×beta is 2x^2 - x - 6.

Answer

The zeroes of the polynomial x2-3x-m(m+3) are

Similar Class 10 Doubts

If a(alph

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?

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 the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta?

If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is?

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