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Let p and q be the two distinct solutions to the equation (x -5)(2x + 9) = x2 -13x + 40.

What is (p + 3)(q + 3)?

Dec 11, 2020

#1
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Let p and q be the two distinct solutions to the equation (x -5)(2x + 9) = x2 -13x + 40.
What is (p + 3)(q + 3)?

Hello Guest!

$$\color{BrickRed}(x -5)(2x + 9) = x^2 -13x + 40\\ 2x^2+9x-10x-45= x^2 -13x + 40\\ x^2+12x-85=0$$

$$x=-6\pm\sqrt{36+85}\\ x=-6\pm 11$$

$$p=5\\ q=-17\\$$

$$(p + 3)(q + 3)=8\cdot (-14)$$

$$(p + 3)(q + 3)=-112$$

!

Dec 12, 2020