Question

Given that the expression 2x² -2.9x-3.6 can be factorized into the form 0.1(px+q)(rx+s), where p, q, r and s are integers, find the value of p + q + r + s. ​

Answer 1

$~~2x^2-2.9x-3.6\\\\=\dfrac{20}{10}x^2 - \dfrac{29}{10} x-\dfrac{36}{10} \\\\=\dfrac 1{10} (20x^2 -29x -361)\\\\=0.1(20x^2-29x-36)\\\\=0.1(20x^2-45x+16x-36)\\\\=0.1[5x(4x-9)+4(4x-9)]\\\\=0.1(5x+4)(4x-9)\\\\\text{Where,}~ p=5, ~ q=4,~ r=4~,s=-9\\\\\text{Hence,}~ \\\\p+q+r+s \\\\ = 5+4+4 -9 \\\\=13-9 \\\\ =4$