Find the roots of the following quadratic equ | vedclass

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(A) Comparing the given equation $x^{2}-5x-1=0$ with the standard form $ax^{2}+bx+c=0$,we get $a=1, b=-5, c=-1$.First,calculate the discriminant $D =

Vedclass · Accepted Answer

$\frac{5+\sqrt{29}}{2}$ and $\frac{5-\sqrt{29}}{2}$

Vedclass · Answer

(A) Comparing the given equation $x^{2}-5x-1=0$ with the standard form $ax^{2}+bx+c=0$,we get $a=1, b=-5, c=-1$.First,calculate the discriminant $D = b^{2}-4ac$:$D = (-5)^{2} - 4(1)(-1) = 25 + 4 = 29$.Since $D > 0$,the equation has two distinct real roots.The quadratic formula is given by $x = \frac{-b \pm \sqrt{D}}{2a}$.Substituting the values:$x = \frac{-(-5) \pm \sqrt{29}}{2(1)} = \frac{5 \pm \sqrt{29}}{2}$.Thus,the roots are $\frac{5+\sqrt{29}}{2}$ and $\frac{5-\sqrt{29}}{2}$.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $x^{2}-5x-1=0$

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