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?
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.