Question

The Sum of the roots of the following equations is 3, and the product of the roots of the equation is 2. Which one is the equation?
A) ${x^2} - 3x + 2 = 0$
B) ${x^2} + 3x + 2 = 0$
C) $3{x^{}} + 6x + 10 = 0$
D) ${x^2} + 3x - 2 = 0$

Answer 1

Hint:The question is related to the quadratic equation. The roots of the quadratic equation are $\alpha + \beta $ and $\alpha .\beta $. And in the equation ${x^2} + (\alpha + \beta )x + \alpha \beta = 0$. Use this identity to solve the question. Solve the question step by step. Make the equation using the sum of the roots and the product of the roots. Here consider the roots of the quadratic equation are $\alpha $ and $\beta $ and solve the question.

Complete step-by-step answer:
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is $ax^2 + bx + c = 0$ with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant "a" cannot be a zero.
Given that
The sum of the roots is 3 and the product of the roots is 2
We have two zero of the equation $\alpha $ and $\beta $
Sum of the roots = 3
$\alpha + \beta $= 3
And the product of the roots = 2
$\alpha .\beta $= 2
We know the general quadratic equation whose roots are $\alpha $ and $\beta $ is given by
${x^2} + (\alpha + \beta )x + \alpha \beta = 0$
Putting the values of and solving the equation we get
${x^2} + 3x + 2 = 0$
Hence, the quadratic equation is ${x^2} + 3x + 2 = 0$

So, the correct answer is “Option B”.

Note:Use the quadratic equation roots for solving the question. A quadratic equation is an equation that can be rearranged in standard from as where x represents an unknown. In the quadratic equation a, b and c are known numbers and x is unknown numbers. In the quadratic equation always solve the variable with variable and the constant term with constant term. Here in this question students make mistakes while taking the roots of the quadratic equation. Always take a quadratic equation equal to zero.