Question

Find the zeros of the polynomial p(z)=z^2-27

Answer 1

Question :

Find the zeros of the polynomial p(z) = z² - 27

Answer:

$+\sqrt{27} \ and \ -\sqrt{27}$

Given :

polynomial, p(z) = z² - 27

To find :

zeroes of the polynomial

Solution :

Given quadratic equation,

      z² - 27

To solve it using factorization method,

 we must know the sum - product pattern

• z² + (0)z - 27

=> It is of the form ax² + bx + c

Find the product of quadratic term [ax²] and constant term [c]

= z² × (-27)

= -27z²

Now, find the factors of "-27z²" in pairs

$=> -z \times 27z \\\\ => -27z \times z \\\\ => 3z \times -9z \\\\ => -3z \times 9z \\\\ => \sqrt{27}z \times -\sqrt{27}z$

Now, from the above, find the pair that adds to get linear term [bx]

√27 z - √27 z = 0

Split 0z as $\sqrt{27} z \ and \ -\sqrt{27} z$

$z^2-27=0 \\\\ z^2+\sqrt{27} z-\sqrt{27} z-27=0$

Find the common factor,

 $z(z+\sqrt{27} ) - \sqrt{27} ( z+\sqrt{27} )=0 \\\\ (z-\sqrt{27} )(z+\sqrt{27} )=0$

=> z - √27 ; z = +√27

=> z + √27 ; z = -√27

     [OR]

SIMPLY :

z² - 27 = 0

  z² = 27

  z = ±√27

$\boxed{\bf{+\sqrt{27} \ and \ -\sqrt{27} \ are \ the \ zeroes \ of \ the \ polynomial.}}$

Answer 2

Step-by-step explanation:

Hope my answer is helpful to u