solve the quadratic equation x^2-3√5x+10=0 AND -x^2+7x-10=0​

Question

solve the quadratic equation x^2-3√5x+10=0 AND -x^2+7x-10=0​

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Amara 3 days 2021-10-11T07:55:25+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-11T07:56:34+00:00

    Solution :-

    (i) x² – 3√5 + 10

    By using :-

     \star \sf{ x = \dfrac{ - b \pm \sqrt{b^2 - 4ac}}{2a} }

    here

    • a = 1

    • b = -3√5

    • c = 10

    \small{ \implies  \sf{ x = \dfrac{ -(-3\sqrt{5}) \pm \sqrt{(-3\sqrt{5})^2 - 4(1)(10)}}{2} } }

     \implies  \sf{ x = \dfrac{ 3\sqrt{5} \pm \sqrt{45 - 40}}{2} }

     \implies  \sf{ x = \dfrac{3\sqrt{5} \pm \sqrt{5}}{2} }

    So x = 2√5 or x = √5

    (ii) -x² + 7x -10

    By using :-

     \star \sf{ x = \dfrac{ - b \pm \sqrt{b^2 - 4ac}}{2a} }

    here

    • a = -1

    • b = 7

    • c = -10

     \implies  \sf{ x = \dfrac{ -(7) \pm \sqrt{(7)^2 - 4(-1)(-10)}}{-2} }

     \implies  \sf{ x = \dfrac{ -7 \pm \sqrt{49 - 40}}{-2} }

     \implies  \sf{ x = \dfrac{-7 \pm \sqrt{9}}{-2} }

     \implies  \sf{ x = \dfrac{-7 \pm 3}{-2} }

    So x = 2 or x = 5

    0
    2021-10-11T07:57:16+00:00

    Step-by-step explanation:

    Given quadratic equation:

    x²-3√5x+10=0

    Splitting the middle term, we

    get

    => x²-2√5x-√5x+10=0

    => x²-2√5x-√5x+2×5=0

    => x²-2√5x+√5x +2×√5×√5=0

    => x(x-2√5)-√5(x-2√5)=0

    => (x-2√5)(x-√5)=0

    => x-2√5 =0 Or x-√5 = 0

    => x = 2√5 Or x = √5

    Therefore,

    Roots of given Quadratic equation are:

    2√5 Or √5

    ………………………………………….

    Hope it was helpful.

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