Question

What constant should be added in given polynomial $x^2-3x+3$ so that it has at least two zeroes

• A. $-3/4$
• B. $2$
• C. $4$
• D. $-4$

Answer 1

The correct option is D $-4$

$x^2-3x+3$

Let the number to be added be equal to $a$, so new polynomial will be

$p\left(x\right)=x^2-3x+3+a$

For two roots, $D>0$

$\Rightarrow D\equiv 9-4(3+a)>0$

$\Rightarrow 4(3+a)<9$

$\Rightarrow 3+a<\frac{9}{4}$

$\Rightarrow a<\frac{9}{4}-3$

$\Rightarrow a<-\frac{3}{4}$.

From options only -4 satisfies this condition.