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If \(Δ \geq 0\), the expression under the square root is non-negative and therefore roots are real. For real roots, we have the following further possibilities. If \(Δ = 0\), the roots are equal and …

When the discriminant of a quadratic equation is greater than 0, it has real and distinct roots. The roots are real and equal if the discriminant value is equal to zero. Hence, if an equation has …

When a, b and c are real numbers, a ≠ 0 and discriminant is positive (i.e., b2 2 - 4ac > 0), then the roots α and β of the quadratic equation ax2 2 + bx + c = 0 are real and unequal. Case II: b2 2 - …

Jul 7, 2023 · Real and Equal Roots: If D is equal to 0, then both the roots will be real and equal and the roots are x=-b, -b. Complex Roots: If D is less than 0, then both the roots will be …

A non-negative discriminant indicates real roots, while a negative one implies complex roots. By analyzing the sum or product of discriminants, we can infer the possible combinations of roots …

Examining the roots of a quadratic equation means to see the type of its roots i.e., whether they are real or imaginary, rational or irrational, equal or unequal. The nature of the roots of a …

In this section, we will examine the roots of a quadratic equation. That is, we will analyze whether the roots of a quadratic equation are equal or unequal, real or imaginary and rational or irrational.

Jan 24, 2023 · We can classify the roots of the quadratic equations into three types using the concept of the discriminant. 1. Two distinct real roots. 2. Two equal real roots. 3. No real roots. …

There are a few ways to tell when a quadratic equation has real roots: Look at the discriminant – if it is positive or zero, the roots are real. Look at the graph – if the parabola touches the x-axis, …

When discriminant equals 0, D = 0 D = 0, we have equal real roots, often called conincident or repeated real roots. When discriminant is a perfect square we have unequal and rational real …

When a, b, c are real numbers, a 0: If = b² -4 a c = 0, then roots are equal (and real). If = b² -4 a c > 0, then roots are real and unequal. If = b² -4 a c < 0, then roots are complex. It is easy to see …

Apr 15, 2018 · If the discriminant is positive and is a perfect square (ex. 36, 121, 100, 625), the roots are rational. If the discriminant is positive and is not a perfect square (ex. 84, 52, 700), …

Addressing whether they are rational / irrational, use the algebra theorem that the root of any prime number is irrational, so if D is prime, then they are irrational. For ax2 + bx + c = 0 a x 2 + …