Question

Jay wants to distribute masks and hand sanitizer bottles in his colony.

The number of masks and bottles distributed in a day can be represented

by the zeroes of the polynomial p(x) = x 2 – 9x + 20.

Answer the questions listed down below.

1. Find the zeroes of p(x)

2. Find the remainder when divided by x+1

3. The value of p(4)

Answer 1

Answer:

1. 4 and 5

2. 30

3. 0

Step-by-Step Explanation:

1.

x² - 9x + 20 = 0

x² - 4x - 5x + 20 = 0

x(x-4) - 5(x-4) = 0

(x-4)(x-5) = 0

x-4 = 0 | x-5 = 0

x = 4 | x = 5

Therefore, the zeroes of the polynomial is 4 and 5.

2.

x + 1 = 0. So, x = -1

p(x) = x² - 9x + 20

p(-1) = (-1)² - 9(-1) + 20

p(-1) = 1 + 9 + 20

p(-1) = 30

Therefore, the remainder when divided by x+1 is 30.

3.

p(x) = x² - 9x + 20

p(4) = (4)² - 9(4) + 20

p(4) = 16 - 36 + 20

p(4) = - 20 + 20

p(4) = 0

Hope this helps you..

Answer 2

1. 4 ,5

2. 30

3. 0

1. Given polynomial is $x^{2} -9x+20$

By mid term splitting method

$x^{2} -5x-4x+20$ =0

x(x-5)-4(x-5) =0 (taking common)

(x-4)(x-5)=0

x-4 =0 and x-5 =0

x=4 and x=5

so the zeroes are 4 ,5

2. p(x) ÷ (x+1)

Put x=-1 in p(x)

p(-1) = $(-1)^{2}-9(-1)+20$     ($(-1)^{2} =1$)

=1+9+20=30

remainder is 30 when divided by x+1

3. p(4) = $4^{2}-9(4)+20$ ($4^{2} =16$ )

=16-36+20 = 0