Find the zeros of the polynomial 6x^2 - 3 - 7x and verify the relationship between the zeros and the coefficients

 Solution of question from book:

Secondary school Mathematics for Class 10 R S Aggarwal V Aggarwal

Unit 2: Algebra

Chapter 2.1: Polynomials

Question :

Find the zeros of the polynomial 6x^2 - 3 - 7x and verify the relationship between the zeros and coefficients.

Solution:

The given polynomial is 6x^2 - 3 - 7x

Rewriting it in the standard form : 6x^2 - 7x - 3

Factorizing it by splitting middle term

= 6x^2 - 9x + 2x - 3

= 3x(2x - 3) + 1(2x - 3)

= (2x - 3)(3x + 1)

Here we get two factors of given polynomial

Using these we get the values of zeros i.e x = 3/2 ad -1/3

Let them be x1 = 3/2 and x2 = -1/3

Verification of sum of zeros and product of zeros

Sum of zeros = -(coefficient of x)/(coefficient of x^2)

and, product of zeros = (constant term)/(coefficient of x^2)

Sum of zeros => 3/2 + (-1/3) = 7/6 ................(i)

which is equal to -(coefficient of x)/(coefficient of x^2) = -(-7)/6 = 7/6 ................(ii)

Now, product of zeros => (3/2)(-1/3) = -1/2 ................(iii)

which is equal to (Constant term)/(Coefficient of x^2) = -3/6 = -1/2 ................(iv)

Using the equations (i), (ii), (iii) and (iv), the relationship between the zeros and the coefficients are verified.

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Question : Find the zeros of the polynomial 6x^2 - 3 - 7x and verify the relationship between the zertos and coefficients.

Solution:

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