Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the cofficients.
${x}^{2} - 2x - 8$

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Answer 1

Answer:

ANSWER

Factorize the equation x

2

−2x−8

Compare equation with ax

2

+bx+c=0

We get, a=1,b=−2,c=−8

To factorize the value we have to find two value which

Sum is equal to, b=−2

product is a×c=1×(−8)=−8

So we can write middle term =2x−4x

We get, x

2

+2x−4x−8

⇒ x(x+2)−4(x+2)

⇒ (x+2)(x−4)

Solve for first zero -

x+2=0

∴ x=−2

Solve for second zero -

x−4=0

∴ x=4

Sum of zero −2+4=2

product of zero 2×(−4)=−8

For equation ax

2

+bx+c=0, if zero are α and β,

Plug the values of a,b and c we get

Sum of zeros

a

−b

=−

1

(−2)

=2

Product of zeros

a

c

=

1

−8

=−8

Hence we have verified that,

Sum of zeros =

Coefficientofx

2

−(Coefficientofx)

Product of zeros =

Coefficientofx

2

Constantterm