Question

• find the zeroes
of polynomial 3² - x - 4. Also verify the
relationship between zeroes and coefficients
​

Answer 1

Answer:

3x² - x - 4

Middle term split :

• 3x² - x - 4
• 3x² + 3x - 4x - 4
• 3x ( x - 1 ) - 4 ( x + 1 )
• ( 3x - 4 ) ( x + 1 )

Zeroes of p(x) :

• 3x - 4 = 0
• 3x = 4
• x = 4/3

Other zero :

• x + 1 = 0
• x = (-1)

➡ Hence zeroes of p(x) are 4/3 and (-1)

Relationship between the zeroes and coffecient :

α + β = (-b/a )

• 4/3 + (-1) = [ - (-1) ] / 3
• 4/3 - 3/3 = 1/3
• 1/3 = 1/3

α x β = c/a

• 4/3 x (-1) = (-4/3)
• (-4/3) = (-4/3)

Hence proved

Answer 2

Answer:-

3x² - x - 4

Middle term split :-

3x² - x - 4

3x² + 3x - 4x - 4

3x ( x - 1 ) - 4 ( x + 1 )

( 3x - 4 ) ( x + 1 )

Zeroes of p(x) :-

3x - 4 = 0

3x = 4

x = 4/3

Other zero :

x + 1 = 0

x = (-1)

➡ Hence zeroes of p(x) are 4/3 and (-1)

Relationship between the zeroes and coffecient :

α + β = (-b/a )

4/3 + (-1) = [ - (-1) ] / 3

4/3 - 3/3 = 1/3

1/3 = 1/3

α x β = c/a

4/3 x (-1) = (-4/3)

(-4/3) = (-4/3)

Hence proved