The least integral value of ' $c$ ' which makes the roots of the equation $x^{2} + 3 x + 2 c = 0$ non real is

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Solution

The correct option is D $2$
The given equation is $x^{2} + 3 x + 2 c = 0$

Here, $A = 1, B = 3$ and $C = 2 c$

For non real roots, we have
$D < 0$
$\Rightarrow B^{2} - 4 A C < 0$
$\Rightarrow B^{2} < 4 A C$
$\Rightarrow 3^{2} < 4 \times 1 \times 2 c$
$\Rightarrow 9 < 8 c$
$2$ is the least integral value of $c$ which satisfies the above inequation.

Hence, the least integral value of $c$ is $2$

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The least integral value of 'c' which makes the roots of the equation x2+3x+2c=0 non real is

The correct option is D 2The given equation is x2+3x+2c=0Here, A=1,B=3 and C=2cFor non real roots, we have D<0⇒B2−4AC<0⇒B2<4AC⇒32<4×1×2c⇒9<8c2 is the least integral value of c which satisfies the above inequation.Hence, the least integral value of c is 2

The least integral value of ' $c$ ' which makes the roots of the equation $x^{2} + 3 x + 2 c = 0$ non real is