Q.

Find the zeroes of the following quadratics Polynomials.

(1)

Sol.

x² – 5x + 6

x²

–

5x

+

6

x² – 5x + 6

=

x²

+

6

–

1

6

6

1

3

2

+

≠

1

+

x

x

=

x

(3x

+

2x)

=

x²

–

3x

–

2x

+

6

=

x

(x

–

3)

–

2

(x

–

3)

=

(x

–

3)

(x

–

2)

(x – 3)

5

5

∴

x

–

3

=

0

or

x

–

2

=

0

∴

x

=

3

or

x

=

2

∴

The zeroes of x² – 5x + 6 are 3 and 2.

∴

(x – 3) and (x – 2) are the factors of

x² – 5x + 6

So, the value of x² – 5x + 6 is zero

When

(x – 3)

=

0

or

(x – 2)

=

0

Q.

Find the zeroes of the following quadratics Polynomials.

(2)

Sol.

x² – 13x – 30

x²

–

13x

–

30

x² – 13x – 30

=

x²

–

30

–

1

30

30

1

15

2

–

≠

13

–

x

x

=

x

(15x

–

2x)

=

x²

–

15x

+

2x

–

30

=

x

(x

–

15)

+

2

(x

–

15)

=

(x

–

15)

(x

+

2)

(x – 15)

13

13

∴

x

–

15

=

0

or

x

+

2

=

0

∴

x

=

15

or

x

=

–2

∴

The zeroes of x² + x – 20 are 15 and –2.

∴

(x – 15) and (x + 2) are the factors of

x² – 13x – 30

So, the value of x² – 13x – 30 is zero

When

(x – 15)

=

0

or

(x + 2)

=

0