$2 z^{2} - 13 z + 15$ =_______

(z - 5) (2 z - 3)

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(z + 5) (2 z - 3)

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(z + 5) (2 z + 3)

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(z - 5) (2 z + 3)

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Solution

The correct option is A $(z - 5) (2 z - 3)$
$2 z^{2} - 13 z + 15$
$= 2 z^{2} - 10 z - 3 z + 15$
$= 2 z (z - 5) - 3 (z - 5)$
$= (z - 5) (2 z - 3)$

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Answer for

3(3z-5)-5(2z-1)=4(2z-3)-17

Factorize: $4 z^{2} - 8 x + 3$
$(a) (2 z - 1) (2 z - 3)$
$(b) (2 z + 1) (3 - 2 z)$
$(c) (2 z + 3) (3 z - 1)$
$(d) (z - 1) (4 z - 3)$

z

C o l u m n - I

a r g (z)

c o l u m n - I I

$C o l u m n - I$ (equation in z)	$C o l u m n - I I$ (principal value of arg(z))
$z^{2} - z + 1 = 0$	$- 2 π / 3$
$z^{2} + z + 1 = 0$	$- π / 3$
${2 z}^{2} + 1 + i \sqrt{3} = 0$	$π / 3$
${2 z}^{2} + 1 - i \sqrt{3} = 0$	$2 π / 3$

arg (z^{1 / 3}) = \frac{1}{2} arg (z^{2} + ¯ z z^{1 / 3})

| z | = 1

z = 3 + 2 i

3 z^{3} - 13 z^{2} + 9 z + 65

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