Question

sum and product of roots polynomial 2*x*x+4x+7​

Answer 1

Answer:

The sum of the roots is -2 and their product is 3.5.

Step-by-step explanation:

$Let\:the\:roots\:be\:\alpha\:and\:\beta.\\Since\:we\:know\:the\:relations\:between\:the\:terms\:and\:the\:zeroes\:of\:an\:equation, \\ \alpha+\beta=-4/2=-2\\\alpha\beta=7/2=3.5$

P.S. If you are not in tenth standard or do not know the relations between terms of the equation and the zeroes, do not worry! You can simply find the roots of the equation and calculate for both values like this:

$2x^2+4x+7=0\\\implies x^2+2x+3.5=0\\\implies x^2+2x=-3.5\\\implies x^2+2x+1^2=-3.5+1^2\\\implies (x+1)^2=-3.5+1\\\implies (x+1)=\sqrt{-2.5}\\\implies x+1=\pm i\sqrt{2.5}\\\implies x=\pm i\sqrt{2.5}-1\\\\So, \:\alpha=i\sqrt{2.5}-1\:and\:\beta=-i\sqrt{2.5}-1\\\\\alpha+\beta=i\sqrt{2.5}-1-i\sqrt{2.5}-1=-2\\\alpha\beta=(-1+i\sqrt{2.5})(-1-i\sqrt{2.5})\\=(-1)^2-(i\sqrt{2.5})^2\\=1-(-2.5)=3.5\\\\Thus,\:\alpha+\beta=-2\:\:and\:\:\alpha\beta=3.5$

Hope it helps!

<3