Question

write the sum of the roots of the quadratic equation 3xsquare-5x+2=0
​

Answer 1

Step-by-step explanation:

Sum = -b/a = -(-5)/3 = 5/3

Answer 2

The sum of the roots of the quadratic equation 3x² - 5x + 2 = 0 is 5/3

Given :

The quadratic equation 3x² - 5x + 2 = 0

To find :

The sum of the roots of the quadratic equation 3x² - 5x + 2 = 0

Solution :

Step 1 of 4 :

Write down the given Quadratic equation

Here the given Quadratic equation is

3x² - 5x + 2 = 0

Step 2 of 4 :

Write down the coefficients

Comparing the given polynomial with general quadratic equation ax² + bx + c = 0 we get

a = 3 , b = - 5, c = 2

Step 3 of 4 :

Find the relation between coefficients and roots

Let roots of the quadratic equation are $\displaystyle \sf{ \alpha , \beta }$

Then we have

$\displaystyle \sf{ \alpha + \beta = - \frac{b}{a} = - \frac{-5}{3} = \frac{5}{3} }$

$\displaystyle \sf{ \alpha \beta = \frac{c}{a} = \frac{2}{3} }$

Step 4 of 4 :

Find sum of the roots of the quadratic equation

Hence sum of the roots of the quadratic equation

$\displaystyle \sf{ = \alpha + \beta }$

$\displaystyle \sf{ = - \frac{b}{a} }$

$\displaystyle \sf{ = - \frac{-5}{3} }$

$\displaystyle \sf{ = \frac{5}{3} }$

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