if the discriminant positive,
then it will have 2 solutions, unequal, real numbers
If the discriminant of a quadratic equation is positive, then the equation has two real roots. The discriminant of a quadratic equation is the part of the quadratic formula underneath the square root symbol, which is given by:
b^2 – 4ac
where a, b, and c are the coefficients of the quadratic equation.
If the discriminant is positive, it means that the value of b^2-4ac is greater than zero. This implies that the square root of the discriminant is a real number, and the quadratic equation will have two distinct real roots (because the roots are given by the quadratic formula: x = (-b +/- sqrt(b^2-4ac))/(2a)).
For example, if we have the quadratic equation:
2x^2 + 5x + 3 = 0
we can calculate the discriminant as:
b^2 – 4ac = (5)^2 – 4(2)(3) = 25 – 24 = 1
Since the discriminant is positive, the quadratic equation has two real roots. To find these roots, we can use the quadratic formula:
x = (-b +/- sqrt(b^2-4ac))/(2a)
x = (-5 +/- sqrt(1))/(2*2)
x = (-5 +/- 1)/4
Therefore, the two roots of the quadratic equation are:
x1 = (-5 + 1)/4 = -3/2
x2 = (-5 – 1)/4 = -1
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