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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 …

Jan 17, 2023 · In algebraic terms, the condition for real and equal roots is expressed as follows: If ax^2 + bx + c = 0, then D = b^2 - 4ac = 0. When the discriminant is equal to zero, then the …

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. …

Learn how to find the condition for roots of quadratic equation to be real or complex, rational or integers. See the formula for discriminant and examples of quadratic equations with different …

If a, b, c, d R show that the roots of the equation (a² +c²) x² +2 (a b +c d) x + (b² +d²) = 0 cannot be real unless they are equal. Determine a positive real value of k such that both the equations …

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 …

If the parabola makes a tangent with the X-axis, then the roots are equal and real, which is also called a double root, which is the point of contact on the X-axis. If the parabola doesn’t touch …

Feb 8, 2025 · Real and Equal Roots. The discriminant is equal to zero, that is, b 2 − 4 a c = 0. The curve intersects the x-axis at only one point. Complex Roots. The discriminant is negative, that …

May 4, 2023 · Real and Equal Roots: If b2 − 4ac = 0 b 2 − 4 a c = 0 then we have only one real root or real roots that are equal.

In this article we discuss the nature of roots depending upon coefficients and discriminant. If α and β are the values of x which satisfy the quadratic equation, α and β are called the roots of the …

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 …

Mar 21, 2024 · In the context of quadratic equations like ax2+bx+c=0, real roots can be found using the quadratic formula: x = (−b ± b2−4ac) /2a. For example, consider the equation …

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 + …

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 …

(i) two distinct real roots, if b 2 – 4ac > 0, (ii) two equal real roots, if b 2 – 4ac = 0, (iii) no real roots, if b 2 – 4ac < 0. Let us consider one examples. Example : Find the discriminant of the …