Question

find the zerows of the polynomial if f(x) =√3x²+5x-8√3 and verify the relationship betweentm the zeroes and its co efficient. ​

Answer 1

Answer:

x = -8/√3 , x = √3

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.

★ To find the zeros of the given polynomial , equate it to zero .

★ If A and B are the zeros of the quadratic polynomial p(x) = 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 ;

f(x) = √3x² + 5x - 8√3

Clearly ,

a = √3

b = 5

c = -8

Now,

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

Thus,

=> f(x) = 0

=> √3x² + 5x - 8√3 = 0

=> √3x² + 8x - 3x - 8√3 = 0

=> x(√3x + 8) - √3(√3x + 8) = 0

=> (√3x + 8)(x - √3) = 0

=> x = -8/√3 , x = √3

Now,

Sum of zeros = -8/√3 + √3

= (-8 + 3)/√3

= -5/√3

Also,

-b/a = -5/√3

Clearly,

Sum of zeros = -b/a

Now,

Product of zeros = (-8/√3)•√3

= -8

Also,

c/a = -8√3/√3 = -8

Clearly,

Product of zeros = c/a

Hence verified.