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Solve the quadratic equation 3x2 + 11x + 10 = 0 using the formula x = -b +/- sqrt(b2-4ac)2a

Mathematics

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Answer

−53,−2-\frac{5}{3}, -2

Step-by-step solution

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दी गई समीकरण है:

3x2+11x+10=03x^2 + 11x + 10 = 0

यह एक द्विघात समीकरण ax2+bx+c=0ax^2 + bx + c = 0 के रूप में है।
यहाँ, a=3a = 3, b=11b = 11, और c=10c = 10 है।

हम द्विघात सूत्र का उपयोग करेंगे:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

  1. aa, bb, और cc के मानों को सूत्र में प्रतिस्थापित करें।

    x=−(11)±(11)2−4(3)(10)2(3)x = \frac{-(11) \pm \sqrt{(11)^2 - 4(3)(10)}}{2(3)}

  2. वर्गमूल के अंदर के मान की गणना करें।

    x=−11±121−1206x = \frac{-11 \pm \sqrt{121 - 120}}{6} x=−11±16x = \frac{-11 \pm \sqrt{1}}{6}

  3. वर्गमूल का मान ज्ञात करें।

    1=1\sqrt{1} = 1 x=−11±16x = \frac{-11 \pm 1}{6}

  4. xx के दो संभावित मानों की गणना करें।

    पहला मान (जब ±\pm के लिए ++ का उपयोग करते हैं):

    x1=−11+16x_1 = \frac{-11 + 1}{6} x1=−106x_1 = \frac{-10}{6} x1=−53x_1 = -\frac{5}{3}

    दूसरा मान (जब ±\pm के लिए −- का उपयोग करते हैं):

    x2=−11−16x_2 = \frac{-11 - 1}{6} x2=−126x_2 = \frac{-12}{6} x2=−2x_2 = -2

    इसलिए, समीकरण के हल हैं:

    x=−53,−2x = \boxed{-\frac{5}{3}, -2}
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