Question

The quadratic equation x² - 6x - 6 = 0 has roots____ + √15, ___-√15​

Answer 1

Answer:

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Answer 2

$\bf{\mathbb{Solution: } \textsf{The Given Equation is \: x² - \ 6x- \ 6=0}}$

Here, a = 1 , b = -6 and , c = 2

${\sf\therefore~ D = b²-4ac }$

${\sf\therefore~ D ={ ( - 6) }^{2} - 4 \times 1 \times ( - 6) }$

${\sf\therefore~ D ={ 36 + 24} }$

${\sf\therefore~ D ={ 60} }$

By Formula

$\sf \implies x=\dfrac{-b±\sqrt{b²-4ac}}{2a}$

$\sf \implies x=\dfrac{-( -6)±\sqrt{ 60}}{2 \times 1}$

$\sf \implies x=\dfrac{6±\sqrt{ 2²×3×5}}{2 }$

$\sf \implies x=\dfrac{ 6±2\sqrt{ 15}}{2}$

$\sf \implies x=\dfrac{ \cancel{2}(3±\sqrt{ 15})}{ \cancel{2}}$

$\sf \implies x=3±\sqrt{ 15}$

$\bf{x= \pink{\boxed3} + \sqrt{15} \quad \: \quad or\quad \quad \: x= \pink{\boxed3} - \sqrt{15} }$