what is discriminant
Answers
Answer:
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. The discriminant of a polynomial is generally defined in terms of a polynomial function of its coefficients.
Answer:
b^2-4ac is called discriminant
Step-by-step explanation:
Case I: b2 – 4ac > 0
When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive, then the roots α and β of the quadratic equation ax2 +bx+ c = 0 are real and unequal.
Case II: b2– 4ac = 0
When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.
Case III: b2– 4ac < 0
When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.
Case IV: b2 – 4ac > 0 and perfect square
When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real, rational and unequal.
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