Algebra
Quadratic Equations
MMTS_Full_Test_12
Grade 12
Question:
If $a,b$ are roots of $x^2-5x+6=0$ and $c,d$ are roots of $x^2-5x+6=0$... Actually: $a,b$ roots of $x^2-px+q=0$ and $c,d$ roots of $x^2-px+r=0$. Then $(a-c)(a-d)(b-c)(b-d)=$
$(q-r)^2$
$(q+r)^2$
$q^2-r^2$
$q-r$
Step-by-Step Solution
Key Concept: $(a-c)(a-d)=a^2-a(c+d)+cd=a^2-ap+r$; similarly for $b$
$(a-c)(a-d)=r-q$; $(b-c)(b-d)=r-q$. Product $=(r-q)^2=(q-r)^2$.
Correct Answer: 1