# 2.6 Quadratic Equations, SPM Practice (Paper 2)

2.6 Quadratic Equations, SPM Practice (Paper 2)

Question 2:
Given α and β are two roots of the quadratic equation (2x + 5)(x + 1) + p = 0 where αβ = 3 and p is a constant.
Find the value p, α and of β.

Solutions:
(2x + 5)(x + 1) + p = 0
2x2 + 2x + 5x + 5 + p = 0
2x2 + 7x + 5 + p = 0
*Compare with, x2– (sum of roots)x + product of roots = 0
Product of roots, αβ = 3
$\frac{5+p}{2}=3$
5 + p = 6
p = 1

Sum of roots = $-\frac{7}{2}$

2+ 6 = 7α ← (multiply both sides with 2α)
2+ 7α + 6 = 0
(2α + 3)(α + 2) = 0
2α + 3 = 0      or        α + 2 = 0
α=− 3 2                       α = –2

Substitute α = –2 into (3),