x² - 3x + 4 = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is x² - 3x + 4 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 1, b = -3 and c = 4
b² - 4ac = (-3)² - 4(1)(4)
= 9 - 16
= -7 < 0
We know that a quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero.
Therefore, the equation has no real roots.
✦ Try This: Determine the nature of the quadratic equation 4x² + x - 1 = 0.
Given, the equation is 4x² + x - 1 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 4, b = 1 and c = -1
b² - 4ac = 1 - 4(4)(-1)
= 1 + 16
= 17 > 0
Therefore, the equation has 2 distinct and real roots
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 1 (i)
x² - 3x + 4 = 0. State whether the following quadratic equation has two distinct real roots
Summary:
The quadratic equation x² - 3x + 4 = 0 has no real roots
☛ Related Questions:
- Which of the following equations has 2 as a root, a. x² - 4x + 5 = 0, b. x² + 3x - 12 = 0, c. 2x² - . . . .
- If 1/2 is a root of the equation x² + kx - 5/4 = 0, then the value of k is, a. 2, b. - 2, c. ¼, d. 1 . . . .
- Which of the following equations has the sum of its roots as 3, a. 2x² - 3x + 6 = 0, b. -x² + 3x - 3 . . . .
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