Find the roots of the quadratic equation usin | vedclass

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Question

(A) The given quadratic equation is $x^{2}-3 \sqrt{5} x+10=0$.Comparing this with the standard form $ax^{2}+bx+c=0$,we get:$a=1, b=-3 \sqrt{5}, c=10$.

Vedclass · Accepted Answer

$2 \sqrt{5}, \sqrt{5}$

Vedclass · Answer

(A) The given quadratic equation is $x^{2}-3 \sqrt{5} x+10=0$.Comparing this with the standard form $ax^{2}+bx+c=0$,we get:$a=1, b=-3 \sqrt{5}, c=10$.The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$.Substituting the values:$x = \frac{-(-3 \sqrt{5}) \pm \sqrt{(-3 \sqrt{5})^{2}-4(1)(10)}}{2(1)}$$x = \frac{3 \sqrt{5} \pm \sqrt{45-40}}{2}$$x = \frac{3 \sqrt{5} \pm \sqrt{5}}{2}$Case $1$: $x = \frac{3 \sqrt{5} + \sqrt{5}}{2} = \frac{4 \sqrt{5}}{2} = 2 \sqrt{5}$.Case $2$: $x = \frac{3 \sqrt{5} - \sqrt{5}}{2} = \frac{2 \sqrt{5}}{2} = \sqrt{5}$.Thus,the roots of the equation are $2 \sqrt{5}$ and $\sqrt{5}$.

Find the roots of the quadratic equation using the quadratic formula:
$x^{2}-3 \sqrt{5} x+10=0$

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Find the roots of the quadratic equation using the quadratic formula:$x^{2}-3 \sqrt{5} x+10=0$