# 2.5.1 Quadratic Equations, SPM Paper 2 (Long Questions)

Question 1:
Solve the quadratic equation, (y + 3)(y – 4) = 30

Solution:

(y + 3)(y – 4) = 30
y2 – 4y + 3y– 12 = 30
y2y – 12 – 30 = 0
y2y – 42 = 0
(y + 6)(y – 7) = 0
y + 6 = 0, y = –6
Or
y – 7 = 0
y = 7

Question 2:
Solve the quadratic equation, 5x2 = 3( x – 2) + 8

Solution:

5x2 = 3x – 6 + 8
5x2 – 3x – 2 = 0
(5x + 2)(x – 1) = 0
5x + 2 = 0, x $-\frac{2}{5}$
Or
x – 1 = 0
x = 1

Question 3:
$\frac{2{p}^{2}-15}{p}=7$

Solution:

$\frac{2{p}^{2}-15}{p}=7$
2p2 – 15 = 7p
2p2 –7p – 15 = 0
(2p + 3)(p – 5) = 0
2p + 3 = 0, p $-\frac{3}{2}$
Or
p – 5 = 0
p = 5

Question 4:
Solve the quadratic equation  $y\left(y-\frac{9}{2}\right)=\frac{5}{2}$

Solution:

$\begin{array}{l}y\left(y-\frac{9}{2}\right)=\frac{5}{2}\\ {y}^{2}-\frac{9y}{2}=\frac{5}{2}\end{array}$

( ×2), 2y2 – 9y= 5
2y2 – 9y – 5 = 0
(2y + 1)(y – 5) = 0
2y + 1 = 0, y = – ½
Or
y – 5 = 0
y = 5