Question

The nature of the root of the quadratic equation 3x²-5x+2=0 are: A)not real. B)real, unequal,rational. C)real, equal, rational​

Answer 1

Answer:

B) real, unequal, rational

Step-by-step explanation:

D=(b)^2 - 4ac

if D is equal to zero then the roots are real and equal

if D is less than zero then the roots are unreal

if D is greater than zero then the roots are real and not equal

in this question b= -5,a=3 and c=2

D=(-5)^2 - 4(3)(2)

D=25-24

D=1 this shows real roots                       now to show if the roots are rational or not

                    use -b+ or - $\sqrt{D}$ and divide the answer with 2(a)

              so we had -(-5)+$\sqrt{1}$ this gives 6 then divide by 2(3) you get 1 which is rational. The other root was -(-5)-$\sqrt{1}$ this gives 4 then divide by 2(3) we get 2/3 which is also rational

Answer 2

Answer:

The nature of the root of the quadratic equation 3x²-5x+2=0 are real, unequal, and rational

Step-by-step explanation:

• A quadratic equation is a type of equation whose degree is two, a quadratic equation can be represented as

                            $ax^{2} +bx+c=0$

• the corresponding root or the value of x that satisfies the quadratic equation is given by the formula

                 $x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$     or $x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

From the question, we have given a quadratic equation of the form

$3x^{2}-5x+2=0$

as compared with the standard equation we get

$a=3\\b=-5\\c=2$

substitute these values to get the roots

$x=\frac{5+\sqrt{25-4*3*2} }{6} =1\\x=\frac{5-\sqrt{25-4*3*2} }{6} =2/3$

that is the values of x are real, unequal, and rational