Multiple choice

The roots of quadratic equation √3 x2+10x+7√3=0 are:

  1. -√3 and 7/√3

  2. √3 and 7/√3

  3. – √3 and (-7)/√3

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation is sqrt(3)x^2 + 10x + 7sqrt(3) = 0. Factoring gives sqrt(3)x^2 + 3x + 7x + 7sqrt(3) = 0, which is sqrt(3)x(x + sqrt(3)) + 7(x + sqrt(3)) = 0. This results in (sqrt(3)x + 7)(x + sqrt(3)) = 0, so the roots are -7/sqrt(3) and -sqrt(3).

AI explanation

We use the method of splitting the middle term to factor the quadratic equation. The product of the coefficient of x^2 and the constant term is the square root of 3 multiplied by 7 times the square root of 3, which equals 21. We need two numbers that multiply to 21 and add to 10, which are 3 and 7; rewriting the middle term gives the square root of 3 times x^2 + 3x + 7 times the square root of 3 times x + 7 times the square root of 3 = 0. Factoring by grouping gives x multiplied by (the square root of 3 times x + 7) plus the square root of 3 multiplied by (the square root of 3 times x + 7) = 0. This simplifies to (x + the square root of 3) multiplied by (the square root of 3 times x + 7) = 0, giving the roots as -1 times the square root of 3 and -7 divided by the square root of 3.

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