Question

The least value of $k$ which makes the roots of the equation $x^2+5x+k=0$ imaginary is

• A. $6$
• B. $7$
• C. $4$
• D. $5$

Answer 1

The correct option is B $7$

We have,

$x^2+5x+k=0$

On comparing with general form of Quadratic Equation $a{x}^2+bx+c=0$

We get $a=1,b=5,c=k$

As roots are imaginary, so $D<0$

$\Rightarrow b^2-4ac<0$

$\Rightarrow (5{)}^2-4(1\left)\right(k)<0$

$\Rightarrow 25-4k<0$

$\Rightarrow 4k>25$

$\Rightarrow k>\frac{25}{4}\approx 6.25$

Hence, the least value of $k$ from the options is $7$.

Option (D) is correct.