Question

sum of roots of quadratic equation x square -4x+2=0 is ________ of products of roots​

Answer 1

The sum of roots of quadratic equation $x^2$ - 4x + 2 = 0 is "equal" to the  products of roots​.

Step-by-step explanation:

The given quadratic equation:

$x^{2}$ - 4x + 2 = 0

Here, a = 1, b = - 4 and c = 2

Let the two roots of the equation = α and β

We know that,

The sum of roots,

α + β = $-\dfrac{b}{a}$

= $-\dfrac{-4}{2}$ = 2

and,

The product of roots, α.β = $\dfrac{c}{a}$

= $\dfrac{2}{1} =2$

∴ The sum of roots = The product of roots = 2

Answer 2

Sum of roots of quadratic equation $x^{2}-4x+2=0$ is twice the product of the roots

• Given quadratic equation is

                     $x^{2}-4x+2=0$

       Here, a = 1, b = -4, c = 2

• Let the roots be $x_{1}, x_{2}$

• We know that,

         sum of roots of quadratic equation = -b/a

                             $x_{1}+x_{2}=\frac{-(-4)}{1}$

                             $x_{1}+x_{2}=4-------(1)$

• Also,

         product of roots of quadratic equation = c/a

                              $x_{1}x_{2}=\frac{2}{1}$

                              $x_{1}x_{2}=2---------(2)$

• From (1) & (2), we get

                               $x_{1}+x_{2}=2(2)=2(x_{1}x_{2})$

∴ Sum of roots is twice the product of the roots for the given quadratic equation.