Question

find the zeroes of the quadratic polynomial x^2+5x+6 and verify the relationship between the zeroes and Coffecients​

Answer 1

Given

We have given a quadratic equation x²+5x+6

To find

we have to find the zeroes of the given quadratic equation and hence, to verify the relationship between it's zeroes and it's coefficients.

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

How to solve :

step 1: First step is to factorise the given equation and find roots.

step 2: After finding the roots (zeroes) ,check the sum of the zeroes and it's product of its zeroes of the Given Equation.

step3: If the sum of its zeroes and product of its zeroes gets equal then the Relationship between the zeroes and coefficients gets verified.

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

=>x²+5x+6

=>x²+3x+2x+6

=>x(x+3)+2(x+3)

=>(x+2)(x+3)=0

x+2=0 and x+3=0

x=-2 or x= -3

zeroes are x= -2 & x= -3

Verifying the relationship between the zeroes and coefficients.

x²+5x+6

zeroes are :α=-2 & β= -3

a= 1 ,b= 5 & c= 6

Sum of its zeroes= -b/a =

α+β= -b/a

-2+(-3)= -5/1

-5= -5

product of its zeroes= c/a

αβ=c/a

-2×-3= 6/1

6=6

L.H.S=R.H.S (Verified)

Answer 2

Answer:

Given

We have given a quadratic equation x²+5x+6

To find

we have to find the zeroes of the given quadratic equation and hence, to verify the relationship between it's zeroes and it's coefficients.

\sf\huge\bold{\underline{\underline{{Solution}}}}

Solution

How to solve :

step 1: First step is to factorise the given equation and find roots.

step 2: After finding the roots (zeroes) ,check the sum of the zeroes and it's product of its zeroes of the Given Equation.

step3: If the sum of its zeroes and product of its zeroes gets equal then the Relationship between the zeroes and coefficients gets verified.

\sf\huge\bold{\underline{\underline{{Solution}}}}

Solution

=>x²+5x+6

=>x²+3x+2x+6

=>x(x+3)+2(x+3)

=>(x+2)(x+3)=0

x+2=0 and x+3=0

x=-2 or x= -3

zeroes are x= -2 & x= -3

Verifying the relationship between the zeroes and coefficients.

x²+5x+6

zeroes are :α=-2 & β= -3

a= 1 ,b= 5 & c= 6

Sum of its zeroes= -b/a =

α+β= -b/a

-2+(-3)= -5/1

-5= -5

product of its zeroes= c/a

αβ=c/a

-2×-3= 6/1

6=6

L.H.S=R.H.S (Verified)