(2a + b)(2c + d)
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b2-4ac
Given 4x2+4x-1 Using the formula for the roots of quadratic equation, (-b +/-./b2-4ac)/2a the roots for the above will be (-4+/-4./2)/8 = (-1+/-./2)/2 Hence the two roots are (-1+./2)/2 and (-1-./2)/2 As the roots are irrational, there is no possibility of getting factors.
trinomials that are prime over the set of rational numbers will NOT factor.A Tinomial ax^2 + bx + c 'will factor' if (b^2-4ac)is a perfect square or zero.
ax2+bx+c=0 with a,b and c real discriminant D=b2-4ac if D >0 then there are 2 real zeros if D = 0 then there is one real zero if D<0 then there are two imaginary zeros There are no other possibility for D For further information search for fundamental theorem of algebra
Let's denote the two consecutive numbers as x and x+1. We can set up the equation x(x+1) = 2756. By expanding the left side of the equation, we get x^2 + x = 2756. Rearranging terms, we have x^2 + x - 2756 = 0. This is a quadratic equation that can be solved using factoring, the quadratic formula, or completing the square to find the two consecutive numbers.