Question

find the zeros of the polynomial √3x^2+5x-8√3

Answer 1

Answer:

$= \: \: \: \: \: \sqrt{3} x {}^{2} + 5x - 8 \sqrt{3} = 0 \\ = \: \: \: \: \: \sqrt{3} x {}^{2} + 8x - 3x - 8 \sqrt{3} = 0 \\ = \: \: \: \: \: x ( \sqrt{3} x + 8) - \sqrt{3} ( \sqrt{3} x + 8) = 0 \\ = \: \: \: \: \: ( \sqrt{3} x + 8)(x - \sqrt{3} ) = 0 \\ \\ = \: \: \: \: \: x = \frac{ - 8}{ \sqrt{3} } = \frac{ - 8 \sqrt{3} }{3} \\ \\ = \: \: \: \: \: x = \sqrt{3}$

Step-by-step explanation:

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Answer 2

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

Hence,

The zeros of the given quadratic polynomial are ; x = -8/√3 , √3

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Moreover :

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.