Question

find the zeros of the polynomial ​

Answer 1

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1)

$p(x) = {x}^{2} - 5x + 6$

LET

$p(x) = 0$

HENCE

${x}^{2} - 5x + 6 = 0$

$x {}^{2} - (3x + 2x) + 6 = 0$

$x {}^{2} - 3x - 2x + 6 = 0$

$x(x - 3) + 2(x - 3) = 0$

$(x - 3)(x + 2) = 0$

HENCE THE ZEROES ARE:-(x-3)AND(x+2).

2)

$p(x) = 0$

$p(x) = {x}^{2} - 5$

$p(x) = {x}^{2} + 0x - 5 = 0$

$( ({x})^{2} - (\sqrt{5} ) {}^{2} ) = 0$

$(x - \sqrt{5} )(x + \sqrt{5} ) = 0$

HENCE THE ZEROES ARE:-(x -root5)AND (x+root5).

3)

$p(x) = 2 {x}^{2} + 3x + 1$

$p(x) = 0$

$2x {}^{2} + 2x + 1x + 1 = 0$

$2x(x + 1) + 1(x + 1) = 0$

$(x + 1)(2x + 1) = 0$

HENCE THE ZEROES ARE :- (x+1) AND (2x+1).

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Answer 2

Solution 1:

Answer:

⇒ x = 2 ____________(i)

⇒ x = 3 ____________(ii)

Step-by-step explanation:

⇒ x² - 5x + 6

⇒ x² - 3x - 2x + 6

⇒ ( x² - 3x ) - ( 2x + 6 )

⇒ x ( x - 3 ) - 2 ( x - 3 )

⇒( x - 2 ) ( x - 3 )

Finding Zeroes :

⇒ ( x - 2 ) = 0

⇒ x = 2 ____________(i)

⇒ ( x - 3 ) = 0

⇒ x = 3 ____________(ii)

Solution 2:

Answer:

⇒ x = 1/√5 ___________(i)

⇒ x = √5 _____________(ii)

Step-by-step-explanation:

⇒ x² - 5

⇒ x² + 0x - 5

⇒ { x² + (√5)² }

⇒ ( x + √5 ) ( x - √5 )

Finding Zeroes :

⇒ ( x + √5 ) = 0

⇒ x = 1/√5 ___________(i)

⇒ ( x - √5 ) = 0

⇒ x = √5 _____________(ii)

Solution 3:

Answer:

⇒ x = -1/2 _____________(i)

⇒ x = - 1 ______________(ii)

Step-by-step-explanation:

⇒ 2x² + 3x + 1

⇒ 2x² + 2x + 1x + 1

⇒ 2x ( x + 1 ) + 1 ( x + 1 )

⇒ ( 2x + 1 ) ( x + 1 )

Finding Zeroes :

⇒ ( 2x + 1 ) = 0

⇒ 2x = - 1

⇒ x = -1/2 _____________(i)

⇒ ( x + 1 ) = 0

⇒ x = - 1 ______________(ii)