### Video Transcript

Find in its simplest form the quadratic equation, whose roots are negative four plus five π and negative four minus five π.

If these are our roots, we can set them equal to π₯ and then we can move them over to the left with π₯ so itβs equal to zero. So when working backwards, we have these factors and we brought them over to the left to be with π₯. Now we can take these two and multiply them together because thatβs what factors do; they multiply together to be our equation.

And now we FOIL. First, we distribute π₯, then we distribute four, and then finally we distribute negative five π. Now we combine like terms. The five ππ₯s cancel; the 20πs cancel. So we have π₯ squared plus eight π₯ plus 16 minus 25π squared.

Now π squared is equal to negative one. So itβs really negative 25 times negative one. So it is actually 25. So we can combine like terms: the 16 and the 25. So our quadratic equation would be π₯ squared plus eight π₯ plus 41.