Question

If the difference of the roots of the quadratic equation is 3 and difference between their cubes is 189, then the quadratic equation is x2±9x+18=0x2±9x+18=0
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Let the roots of the equation be a and b
then, $a^3-b^3=189$
and $a-b=3$
cubing both sides:
$(a-b{)}^3=27$
$a^3-b^3-3ab(a-b)=27$
$189-3ab\left(3\right)=27$
$162=9ab$
$ab=18$
Similarly, $(a+b{)}^2=(a-b{)}^2+4ab$
$(a+b{)}^2=3^2+4(18)$
$(a+b{)}^2=9+72$
$a+b=\pm 9$
The general form of equation is $x^2-Sx+P=0$, hence the equation will be
$x^2\pm 9x+18=0$