Question

Verify relationship between zero and its co-efficient 6x-x-2

Answer 1

Answer:

x = 2/3 , -1/2

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ In order to find the zeros of the polynomial ,equate it to zero and find the possible values of the variable .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution:

Here,

The given quadratic polynomial is ;

6x² - x - 2

On comparing the given quadratic polynomial with the general form ax² + bx + c ,

We have ;

a = 6

b = -1

c = -2

Now,

Let's find the zeros of the given quadratic polynomial by equating it to zero .

Thus,

=> 6x² - x - 2 = 0

=> 6x² - 4x + 3x - 2 = 0

=> 2x(3x - 2) + (3x - 2) = 0

=> (3x - 2)(2x + 1) = 0

=> x = 2/3 , -1/2

Hence,

The zeros of the given quadratic polynomial are : x = 2/3 , -1/2 .

Now,

Sum of zeros = 2/3 + (-1/2)

= 2/3 - 1/2

= (4 - 3)/6

= 1/6

Also ,

-b/a = -(-1)/6 = 1/6

Hence,

Sum of zeros = -b/a

Now,

Product of zeros = (2/3)×(-1/2) = -1/3

Also,

c/a = -2/6 = -1/3

Hence,

Product of zeros = c/a

Hence verified .