How many and what type of solutions does the equation have? –4x^2 – 2 = 10x A. no real solutions B. one real solution C. two rational solutions D. two irrational solutions

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How many and what type of solutions does the equation have? –4x^2 – 2 = 10x A. no real solutions B. one real solution C. two rational solutions D. two irrational solutions

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Answer 1 · 2016-03-11T14:55:34

2 real roots

Explanation:

$y = - 4 x^{2} - 10 x - 2 = 0 .$ $y = -4x^2 - 10x - 2 = 0.$ Transform the equation to -->
$y = 2 x^{2} + 5 x + 1 = 0$ $y = 2x^2 + 5x + 1 = 0$
$D = d^{2} = b^{2} - 4 a c = 25 - 8 = 17$ $D = d^2 = b^2 - 4ac = 25 - 8 = 17$ --> $d = \pm \sqrt{17}$ $d = +- sqrt17$
There are 2 real roots;
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} =$ $x = -b/(2a) +- d/(2a) =$
$x = - \frac{5}{4} \pm \frac{\sqrt{7}}{4}$ $x = - 5/4 +- sqrt7/4$

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How many and what type of solutions does the equation have? –4x^2 – 2 = 10x A. no real solutions B. one real solution C. two rational solutions D. two irrational solutions

1 Answer

Explanation:

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