Question

A quadratic polynomial when divided by (x – 21), gives remainder 71 and when divided by (x – 71), gives remainder 21, then the polynomial can be​

Answer 1

Answer:

A quadratic polynomial is a function with degree 2, that is, the highest power is 2. The general formula for the quadratic equation is:

$ax^{2} +bx + c$

where a and b are coefficients of the variables and c is constant.

Explanation:

For the given problem, we first need to determine the factors. (x-21) and   (x-71) give 71 and 21 as remainders respectively.

Hence, we get two factors of the equation by adding the remainder to the divisor.

After that, we only need to multiply the factors and get our quadratic equation.

Let's do it:

1. Factors are calculated as explained:

$i. (x-21) + 71 = (x+50)\\ii. (x-71) + 21 = (x-50)$   - (a)

2. Multiply the factors:

$(x+50)(x-50) = x^{2} -(50)^2$  - (b)

using the algebraic identity of $x^{2} - y^2 = (x+y)(x-y)$

Now the answer to equation b is:

$x^{2} -2500$

Hence, the quadratic equation for the given question is :

$x^{2} -2500=0$

If you want to solve it further for x, you get:

$x^{2} =2500\\x = 50$