If a and b are the roots of the quadric polynomial 2x^2+6x+7 what are a+b and ab?
The phrase "a and b are roots of 2x^2+6x+7" is just a way of saying that x=a and x=b solve the equation 2x^2+6x+7=0. Check out that by diving by 2 on both sides of this equation we get that that x=a and x=b solve x^2+3x+3.5=0. So a and b are roots of the polynomial x^2+3x+3.5, which has leading coefficient 1. Therefore it can be written as x^2+3x+3.5=(x-a)(x-b)=x^2-(a+b)x+ab. Equating coefficients of same degree: a+b=-3 ab=3.5
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