Question

Find the zeroes of the quadratic polynomial x
${x}^{2}$
- 13x + 40 and verify the relationship
between the zeroes and the coefficients of the polynomial.​

Answer 1

Answer:

The given polynomial is x

2

+14x+48

By factorising the quadratic polynomial we get, x

2

+14x+48=(x+8)(x+6)

The value of x

2

+14x+48 is zero, When x+8=0 or x+6=0.

That is, when x=−8 or x=−6

The zeroes of the polynomial x

2

+14x+48 are −8 and −6.

Let us verify the results by substituting the values.

p(x)=x

2

+14x+48=(−8)

2

+14(−8)+48=64−112+48=0∴p(−8)=0

p(−6)=(−6)

2

+14(−6)+48=36−84+48∴p(−6)=0