Question

Find the value of discriminant of the following Equation.
$2{x^2} + x + 1 = 0$
$\left( A \right)7$
$\left( B \right) - 7$
$\left( C \right)9$
$\left( D \right) - 9$

Answer 1

Here, given to find the discriminant of a quadratic equation. For example, let’s assume $a{x^2} + bx + c = 0$is an equation, and we have to find the discriminant of this equation. So, discriminant of equation denoted by $'\Delta '$and the formula for this is,
$\Rightarrow \Delta = {b^2} - 4ac$ .

Complete step-by-step solution:
The given equation in the question is
$2{x^2} + x + 1 = 0$_ _ _ _ _ _ _ _ _ $\left( 1 \right)$
To find the discriminant we have to compare the equation$\left( 1 \right)$ with,
$a{x^2} + bx + c = 0$ _ _ _ _ _ _ _ _ _$\left( 2 \right)$
Compare $\left( 1 \right)$and $\left( 2 \right)$,
$\Rightarrow a = 2,b = 1,c = 1$
Substitute the values in formula,
$\begin{aligned} &\Rightarrow \Delta = {b^2} - 4ac \\\ &\Rightarrow \Delta = {\left( 1 \right)^2} - 4 \times 2 \times 1 \\\ &\Rightarrow \Delta = 1 - 8 \\\ &\Rightarrow \Delta = - 7 \\\ \end{aligned}$
Therefore, the value of the discriminant is $\Delta = - 7$ and the correct option is $\left( B \right)$.

Note: $\Rightarrow$ If the discriminant value is positive, the quadratic equation has two real and distinct solutions.
$\Rightarrow$ If the discriminant value is zero, the quadratic equation has only one solution or two real and equal solutions.
$\Rightarrow$ If the discriminant value is negative, the quadratic equation has no real.