Question

Find the nature of the roots of 4x^2 + 10x + 6 = 0.

Answer 1

Rational

Step-by-step explanation

Step 1

to find the nature of the roots of the quadratic equation, we will first calculate the roots of the equation.

`4x^2+10x+6=0`

to solve for x, we can use the quadratic formula

remember:

`\begin{gathered} \text{ for} \\ ax^2+bx+c=0 \\ th\text{e solutino for x is} \\ x=(-b\pm√(b^2-4ac))/(2a) \end{gathered}`

now, the discriminant is

`b^2-4ac`

so, to check the nature of the roots we have these criteria

so, let

`\begin{gathered} ax^2+bx+c==\Rightarrow4x^2+10x+6=0 \\ so \\ a=4 \\ b=10 \\ c=6 \end{gathered}`

now, replace in the discriminat formula

`\begin{gathered} b^2-4ac \\ (10^2)-4(4)(6) \\ 100-96 \\ 4 \end{gathered}`

so, the discrimant is 4, therefore

`\begin{gathered} b^(2)-4ac\gt0 \\ 4>0\Rightarrow \end{gathered}`

Rational

I hope this helps you