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Grade 11Algebra

find for what value of a equation x^2 + 2x -(a^3 -3a - 3) = 0 has real roots

SuperGaming SuperheroGeek

8 Years agoGrade 11

1 Answer

venkat

8 Years ago

$\Delta \geq 0$ for the equation to have real roots.

$\sqrt{B^2-4AC}\geq 0$

here A=1 B=2 C=a²-3a-3

$\sqrt{(2)^2-4(1)(a^{2}-3a-3)}\geq 0$

$\sqrt{4-4(a^{2}-3a-3)}\geq 0$

$2\sqrt{1-(a^{2}-3a-3)}\geq 0$

$\sqrt{-a^{2}+3a+4}\geq 0$

${-a^{2}+3a+4}\geq 0$

${a^{2}-3a-4}\leq 0$

$a^{2}-4a+a-4\leq 0$

$a(a-4)+1(a-4)\leq 0$

$(a+1)(a-4)\leq 0$

$-1\leq a\leq 4$

$\therefore a\ \epsilon \ [-1,4] \ for \ the \ given \ equation \ to \ have \ real \ roots$

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