Question

Solve this problem..........

Find the zeros of a given polynomial and verify the relationship between the zeros and coefficients of polynomial.

a). 9x²-5​

Answer 1

Answer:

x = ± √5 / 3

Note:

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

• To find the zeros of any polynomial, equate it to zero.

• If A and B are the zeros of the quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

Solution:

Here,

The given quadratic polynomial is :

9x² - 5 .

The given quadratic polynomial can be rewritten as : 9x² + 0x - 5 .

Clearly ,

a = 9

b = 9

c = 5

Now,

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

Thus,

=> 9x² - 5 = 0

=> 9x² = 5

=> x² = 5/9

=> x = √(5/9)

=> x = ± √5/3

Now,

Sum of zeros = √5/3 + (-√5/3)

= √5/3 -√5/3

= 0

Also ,

-b/a = 0/9 = 0

Clearly ,

Sum of zeros = -b/a (Hence verified)

Now,

Product of zeros = (√5/3)(-√5/3)

= - 5/9

Also,

c/a = -5/9

Clearly ,

Product of zeros = c/a (Hence verified)