Question

Zeroes of a quadratic polynomial are 3 and 7. Find the remainder when this polynomial is divided by x 2 − 5x + 6.

Answer 1

Answer:

Zeroes of the polynomial = 3, 7

sum of zeroes = 3+7 =1 0

product of zeroes = 3*7 = 21

p(x) = x^2 - 10x + 21

to find the remainder we have 5o divide

x^2 - 5x + 6 / x^2 - 10x + 21

( division is shown in picture)

Answer 2

Answer:

The remainder is 15x+15.

Step-by-step explanation:

Given: Zeroes of the polynomial are 3 & 7 and it is divided by $x^{2} -5x+6$.

To find the remainder.

We know that 2 degree polynomial equation is given by:

$x^{2} +(\text{sum of zeroes})x+\text{product of zeroes}$

Here, zeroes are 3 & 7.

=> Sum of zeroes= 3+7=10

And product of zeroes = 3(7)=21

So, polynomial is: $x^{2} +10x+21$.

Now to find the remainder divide $x^{2} +10x+21$ by $x^{2} -5x+6$.

$x^{2} -5x+6$ ) $x^{2} +10x+21$ ( 1

                   $x^{2} -5x+6$

               -        +       -

               ________________

                                15x+15

               _________________

Therefore, the remainder is 15x+15.

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