# Question Video: Forming a Quadratic Equation in the Simplest Form given Its Roots Involving Complex Numbers Mathematics • 10th Grade

Find in its simplest form, the quadratic equation whose roots are โ4 + 5๐ and โ4 โ 5๐.

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### Video Transcript

Find in its simplest form the quadratic equation, whose roots are negative four plus five ๐ and negative four minus five ๐.

If these are our roots, we can set them equal to ๐ฅ and then we can move them over to the left with ๐ฅ so itโs equal to zero. So when working backwards, we have these factors and we brought them over to the left to be with ๐ฅ. Now we can take these two and multiply them together because thatโs what factors do; they multiply together to be our equation.

And now we FOIL. First, we distribute ๐ฅ, then we distribute four, and then finally we distribute negative five ๐. Now we combine like terms. The five ๐๐ฅs cancel; the 20๐s cancel. So we have ๐ฅ squared plus eight ๐ฅ plus 16 minus 25๐ squared.

Now ๐ squared is equal to negative one. So itโs 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 ๐ฅ squared plus eight ๐ฅ plus 41.