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Polynomial Arithmetic

Solving Identity Equations


How many real values of xx satisfy the following equation 9x63x55=09^x - 6 \cdot 3^x - 55 = 0?

If the equation 3x+4y+5=ax+by+c=dxeyf3x+4y+5=ax+by+c=-dx-ey-f holds for all numbers xx and yy, what is the value of cfbeadcf-be-ad?

Given that ax+4y+cz+23=7x+by+4z+dax+4y+cz+23=7x+by+4z+d is an algebraic identity in xx, yy and zz, what is the value of a+b+c+da+b+c+d?

Given that ax2+bx+c+7x2+8x12=0ax^2+bx+c+7x^2+8x-12=0 is an algebraic identity, what is the value of abcabc?

If the following holds for all real numbers xx and yy, (ax+by+c)+(5x+5y19)=0,(ax+by+c)+(5x+5y-19)=0, what is the value of a+b+ca+b+c?


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