Question

What is the discriminant of $3{{x}^{2}}+6x=2?$

Answer 1

Hint: We solve this question by using the discriminant formula $D={{b}^{2}}-4ac$ for the given equation in question. Before that we rearrange the equation in the question to a standard form given by $a{{x}^{2}}+bx+c.$ We then compare the coefficients of the two equations. Using the coefficients in the discriminant formula, we obtain a value which is nothing but the discriminant for the quadratic equation.

Complete step by step solution:
In order to solve this question, let us first convert the given equation in the question to the standard form of a quadratic equation. The standard form of a quadratic equation is given by $a{{x}^{2}}+bx+c=0.$ Now, the equation given in the question is
$\Rightarrow 3{{x}^{2}}+6x=2$
To convert this to the standard form, we subtract both sides by 2.
$\Rightarrow 3{{x}^{2}}+6x-2=2-2$
Subtracting the terms on the right-hand side of the equation, we obtain the standard form of a quadratic equation.
$\Rightarrow 3{{x}^{2}}+6x-2=0$
Comparing this with the standard quadratic equation, we can see the coefficients are $a=3,b=6,c=-2.$
We now use the formula to calculate the discriminant given by
$\Rightarrow D={{b}^{2}}-4ac$
Substituting the obtained values of $a,b,c$ in the above equation,
$\Rightarrow D={{6}^{2}}-4\times 3\times -2$
Multiplying the terms in the second term and substituting the square of 6 in the above equation,
$\Rightarrow D=36+24$
Adding the two terms,
$\Rightarrow D=60$

Hence, the discriminant for the equation $3{{x}^{2}}+6x=2$ is found to be 60.

Note:
We need to know the discriminant and its formula to solve this sum. The discriminant is used to obtain the roots of the quadratic equation. The roots of a quadratic equation are obtained by using the formula $x=\dfrac{-b\pm \sqrt{D}}{2a},$ where D is the discriminant of the quadratic equation given by the formula $D={{b}^{2}}-4ac.$