Question

find the zeroes of the polynomial 49x^2-64

Answer 1

Step-by-step explanation:

We know that, 49 is the square of 7 and 64 is the square of 8. To find the zeroes, we have to use zero product rule. Hence, the zeroes are - 8/7 and 8/7.

49

x

2

−

64

=

0

or

(

7

x

)

2

−

(

8

)

2

=

0

or

(

7

x

+

8

)

(

7

x

−

8

)

=

0

∴

(

7

x

−

8

)

=

0

or

(

7

x

+

8

)

=

0

∴

x

=

8

7

or

x

=

−

8

7

Usually we make a quadratic equal to 0 to be able to solve it.

This is an exception, where we can use the normal method of x on one side and the numbers on the other.

49

x

2

=

64

x

2

=

64

49

find the square root of both sides

x

=

±

√

64

49

x

=

=

8

7

or

x

=

−

8

7

However, we can also use the factorising method:

49

x

2

−

64

=

0

the difference of two squares

(

7

x

+

8

)

(

7

x

−

8

)

=

0

x

=

−

8

7

or

x

=

8

7