Solutions — 5J Worksheet
Year 10 Mathematics Core · Cambridge Ch 5, §5J · Mr Wong
ANSWER KEY
Warm-up — discriminant
Q1. $\Delta=b^2-4ac$ and number of real solutions:
a $\Delta=0$, one
b $\Delta=-16$, none
c $\Delta=17$, two
d $\Delta=0$, one
Part A — Solving with the formula
Q2.
a $x=\dfrac{-3\pm\sqrt{21}}{2}$
b $x=2\pm\sqrt3$
Part B — Non-monic with the formula
Q3.
a $x=\dfrac{-5\pm\sqrt{17}}{4}$
b $x=\dfrac{1\pm\sqrt7}{3}$
Part C — How many solutions?
Q4.
a two $\Delta=37$
b none $\Delta=-23$
c one $\Delta=0$
d two $\Delta=53$
Part D — Mixed
Q5. $x^2+5x+3=0$:
· $x=\dfrac{-5\pm\sqrt{25-12}}{2}=$ $\dfrac{-5\pm\sqrt{13}}{2}$
Q6. $2x^2-2x-1=0$:
· $x=\dfrac{2\pm\sqrt{4+8}}{4}=\dfrac{2\pm 2\sqrt3}{4}=$ $\dfrac{1\pm\sqrt3}{2}$
Challenge
Q7. $x^2+kx+9=0$ has one real solution when $\Delta=0$:
· $k^2-4(1)(9)=0 \Rightarrow k^2=36 \Rightarrow$ $k=6$ or $k=-6$.