Question

A quadratic polynomial having sum and product of its zeroes as 5 and 0 respectively, is​

Answer 1

Answer:

$x ^{2} - 5x$

Step-by-step explanation:

$x ^{2} - (\alpha + \beta )x + \alpha \beta \\ x ^{2} - 5x + 0 \\ = x ^{2} - 5x$

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Answer 2

Answer:

• A polynomial of degree 2 is referred to as a quadratic polynomial and can be expressed as ax2 + bx + c, where a, b, and c are integers.
• The numbers of x that bring a quadratic equation to zero are known as its zeroes.
• The product of the zeroes is given by c/a, and the total of the zeroes is given by -b/a if the zeroes of a quadratic equation are and.
• Given knowledge states that the product of zeroes equals zero and the total of zeroes equals five.
• At least one of the zeroes must be zero if the sum of the zeroes is 0.
• Suppose that is one of the zeros, in which case = 5 -. (since the sum of the zeroes is 5).
• We have = 0, which means that either = 0 or = 0, since the sum of the numbers is 0.
• The quadratic polynomial can be written as x(x - 5) = x2 - 5x if = 0, then = 5, and so on.
• The quadratic polynomial can be written as x(x - 5) = x2 - 5x if = 0, then = 5, and so on.

Therefore, x2 - 5x, which has values 0 and 5, is the necessary quadratic equation and complies with the requirements.

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