Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x2 + 2x + 7 = 21 The number of posi

Question

Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x2 + 2x + 7 = 21 The number of positive solutions to this equation is . The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is .

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Amaya 2 weeks 2021-09-12T05:33:56+00:00 2 Answers 0

Answers ( )

    0
    2021-09-12T05:35:17+00:00

    Answer:

    (a) 1

    (b) 1

    (c) 3.03

    Step-by-step explanation:

    The given quadratic equation is

    Subtract 27 from both sides.

    Taking out common factor.

    Divide both sides by 4.

    If an expression is , then we need to add , to make it perfect square.

    Here, b=2, so

    Add 1 on both sides.

    Taking square root on both sides.

    Subtract 1 from both sides.

    and

    and

    Only one solution is positive.

    Greatest solution is 3.031, therefore the approximate value of this solution is 3.03.

    0
    2021-09-12T05:35:21+00:00

    Answer:

    This quadratic equation has only 1 positive solution, and the greatest solution is 2.87, rounded to the nearest hundredth.

    Step-by-step explanation:

    The given expression is

    x^{2}+2x+7=21

    To solve this expression, we need to pass all terms to the left side

    x^{2}+2x+7=21\\x^{2}+2x+7-21=0\\x^{2}+2x-14=0

    Now, we solve the equation using the quadratic formula

    x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac} }{2a}

    Where

    a=1\\b=2\\c=-14

    Replacing these values, we have

    x_{1,2}=\frac{-2\±\sqrt{2^{2}-4(1)(-14)} }{2(1)}\\x_{1,2}=\frac{-2\±\sqrt{4+56} }{2}=\frac{-2\±\sqrt{60} }{2}  \\x_{1}\approx 2.9\\x_{2}\approx -4.9

    Therefore, this quadratic equation has only 1 positive solution, and the greatest solution is 2.87, rounded to the nearest hundredth.

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27:3+15-4x7+3-1=? ( )