Question

The zeroes of square of polynomial $x^2+5x+6$ are ______ .

• A. -2 & -3
• B. 4 & 9
• C. -4 & -9
• D. 2 & 3

Answer 1

The correct option is A -2 & -3

Given, $x^2+5x+6$
Lets factorise before squaring.
$x^2+5x+6$ $=x^2+3x+2x+6x(x+3)+2(x+3)(x+2)(x+3)$

Squaring: $x^2+5x+6$
$(x^2+5x+6{)}^2$$={\left[\right(x+2\left)\right(x+3\left)\right]}^2=(x+2{)}^2(x+3{)}^2$

Lets find zeroes,
$(x+2{)}^2=0;(x+3{)}^2=0$
Take square root on both side.
$x+2=0;x+3=0x=-2;-3$

Zeroes are -2 and -3.

Conclusion: Roots of the equation will be same.
$x^2+5x+6=(x+2)(x+3)$
Zeroes are $x=-2;-3$