Question

Find the quadratic polynomial whose zeroes are 2/3 and -1 / 4 . Verify the relationship between zeroes and co efficient

Answer 1

Here is your solution :

Given,

Zeroes = ( 2/3 ) and ( -1/4 )

We know the formula for a quadratic equation :

⇒ x² - ( Sum of zeroes )x + Product of zeroes = 0

Now , we have to find the sum of zeroes and product of zeroes .

Here we go,

⇒ Sum of zeroes = ( 2/3 ) + ( -1/4 )

= ( 2/3 ) - ( 1/4 )

= ( 8 - 3 ) / 12

= 5/12

And,

⇒ Product of zeroes = ( 2/3 ) ( -1/4 )

= ( -1/6 )

Now , plug these values in the above used formula.

⇒ x² - ( 5/12 )x + ( -1/6 ) = 0

⇒ ( 12x² - 5x - 2 ) / 12 = 0

⇒ 12x² - 5x - 2 = 0 × 12

⇒ 12x² - 5x - 2 = 0

Hence,

The required Quadratic Equation is :

⇒ 12x² - 5x - 2 = 0

Here,

Coefficient of x² ( a ) = 12

Coefficient of x( b ) = -5

Constant term ( c ) = -2

Now,

⇒ Sum of zeroes = -b/a

⇒5/12 = - ( -5 ) / 12

•°• 5/12 = 5/12

And,

⇒ Product of zeroes = c/a

⇒-1/6 = -2/12

•°• -1/6 = -1/6

Verified !!

Answer 2

Answer:

Step-by-step explanation:

Here is your solution :

Given,

Zeroes = ( 2/3 ) and ( -1/4 )

We know the formula for a quadratic equation :

⇒ x² - ( Sum of zeroes )x + Product of zeroes = 0

Now , we have to find the sum of zeroes and product of zeroes .

Here we go,

⇒ Sum of zeroes = ( 2/3 ) + ( -1/4 )

= ( 2/3 ) - ( 1/4 )

= ( 8 - 3 ) / 12

= 5/12

And,

⇒ Product of zeroes = ( 2/3 ) ( -1/4 )

= ( -1/6 )

Now , plug these values in the above used formula.

⇒ x² - ( 5/12 )x + ( -1/6 ) = 0

⇒ ( 12x² - 5x - 2 ) / 12 = 0

⇒ 12x² - 5x - 2 = 0 × 12

⇒ 12x² - 5x - 2 = 0

Hence,

The required Quadratic Equation is :

⇒ 12x² - 5x - 2 = 0

Here,

Coefficient of x² ( a ) = 12

Coefficient of x( b ) = -5

Constant term ( c ) = -2

Now,

⇒ Sum of zeroes = -b/a

⇒5/12 = - ( -5 ) / 12

•°• 5/12 = 5/12

And,

⇒ Product of zeroes = c/a

⇒-1/6 = -2/12

•°• -1/6 = -1/6

thank u