CEMC Fermat, 2025

Algebra Difficulty 1.4 Junior Find the answer Canada

If the equation $(x+2)(x+t)= x^2 + bx + 12$ is true for all real numbers $x$ , the value of $b$ is

Pick one

Solution

Since the equation is true for all real numbers $x$ , it is true for $x=0$ .

Substituting $x=0$ , we get $(0+2)(0+t)=0^2+b(0)+12$ or $2t=12$ , and so $t=6$ .

The equation becomes $(x+2)(x+6)=x^2+bx+12$ or $x^2+8x+12=x^2+bx+12$ , and so $b=8$ .

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