Question

Write the equation of the polynomial with the following zeros in standard form

Answer 1

x² - (5 + √7)x + 5√7

Step-by-step explanation:

A polynomial with zeros at x = a and x = b can be written as:

(x - a)(x - b)

So, if the roots are x = √7 and x = 5, we can write the equation for the polynomial as follows:

(x - √7)(x - 5)

Then, to write it in standard form, we need to apply the distributive property, so:

`\begin{gathered} (x-\sqrt[]{7})(x-5)=x\cdot x+x(-5)-\sqrt[]{7}x-\sqrt[]{7}(-5) \\ (x-\sqrt[]{7})(x-5)=x^2-5x-\sqrt[]{7}x+5\sqrt[]{7} \\ (x-\sqrt[]{7})(x-5)=x^2-(5+\sqrt[]{7})_{}x+5\sqrt[]{7} \end{gathered}`

Therefore, the answer is:

x² - (5 + √7)x + 5√7