Question

Example 2 Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the
V relationship between the zeroes and the coefficients.​

Answer 1

Answer:

Let

p(x)=x

2

+7x+10

comparing with p(x)=ax

2

+bx+c

a=1,b=7,c=10

p(x)=x

2

+7x+10

⇒x

2

+5x+2x+10

⇒x(x+5)+2(x+5)

⇒(x+2)(x+5)

Let p(x)=0

⇒(x+2)(x+5)=0

x=−2,5

α=−2,β=−5

a

−b

=α+β⇒

1

−(7)

=−7

a

c

=α⋅β⇒

1

10

=10

Answer 2

Step-by-step explanation:

Let

p(x)=x

2

+7x+10

comparing with p(x)=ax

2

+bx+c

a=1,b=7,c=10

p(x)=x

2

+7x+10

⇒x

2

+5x+2x+10

⇒x(x+5)+2(x+5)

⇒(x+2)(x+5)

Let p(x)=0

⇒(x+2)(x+5)=0

x=−2,5

α=−2,β=−5

a

−b

=α+β⇒

1

−(7)

=−7

a

c

=α⋅β⇒

1

10

=10