the quadratic equation 3x^2-7x=3 has roots that are...1.)real, rational, and equal 2.)real, rational and unequal 3.)real, irrational and unequal 4.)imaginary AND WHY?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the quadratic equation:

3x^2 - 7x = 3

==> 3x^2 - 7x -3 = 0

We need to determine the type of roots.

Then, we will use the discriminant to find out.

We know that:

delta = b^2 - 4ac

If delta = 0 ==> then the equation has one real root.

If delta > 0 ==> then the equation has two real roots.

If delta < 0 then the equation has two complex roots.

If delta is a complete square, then it has 2 rational roots

If delta is not a complete square, then it has 2 irrational roots.

Let us test delta.

delta = b^2 -4ac = (-7)^2 - 4*3*-3 = 49 + 36 = 85

Then delta > 0 , then it has two real roots.

Also, delta is NOT a complete square, then it has irrational roots.

Then, the answer is number (3) Real, irrational, and unequal.

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