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The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.

Mar 1, 2025 · In a quadratic equation ax2 + bx + c = 0, a ≠ 0, we have seen that the roots of this equation are given by α = − b + √b2 − 4ac 2a and β = − b − √b2 − 4ac 2a. The expression …

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. …

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them : It has no real roots. It has equal real roots. It has two distinct real roots. We cannot factorize …

Oct 21, 2024 · Example 1: Without solving, examine the nature of roots of the equation 2x 2 + 2x + 3 = 0. Sol. Comparing 2x 2 + 2x + 3 = 0 with ax 2 + bx + c = 0 we get: a = 2, b = 2 and c = 3 D …

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 …

Feb 8, 2025 · Let’s see the steps on how we can find the nature of roots with an example. Step 1: Compare the given quadratic equation with the standard form of quadratic equations $a x^2+b …

Various types of Solved examples on nature of the roots of a quadratic equation: 1. Find the nature of the roots of the equation 3x\(^{2}\) - 10x + 3 = 0 without actually solving them.

Directions: Read carefully and choose the best answer. 1. 2. Which equation has imaginary roots? 3. Given the equation x2 + 3 x - 9 = 0. What is the product of the roots? 4. Which equation has …

Jul 7, 2023 · Let us now learn the above method with examples to find the nature of the roots of a quadratic equation. Example 1: Find the nature of the roots of x 2 +2x+5=0. Comparing the …

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 …

Method 1: The roots of the quadratic equations can be found by the Shridharacharaya formula. Example: The length of sides of a rectangle is given by x – 3 and x – 5 and the area of the …

Here you will learn how to find the nature of roots of quadratic equation using discriminant with examples. Let’s begin –. (a) Consider the quadratic equation ax2 + bx + c a x 2 + b x + c = 0 …

6 days ago · The roots within 1 cm below the root–hypocotyl junction were embedded in 5% agarose and sectioned by vibratome at 100-µm thickness. The sections were mounted with …