√2x² - 3/√2x + 1/√2 = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is √2x² - 3/√2x + 1/√2 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = √2, b = -3/√2 and c = 1/√2
b² - 4ac = (-3/√2)² - 4(√2)(1/√2)
= 9/2 - 4
= (9 - 8)/4
= 1/4 > 0
We know that a quadratic equation ax² + bx + c = 0 has real and distinct roots when the discriminant of the equation is greater than zero.
Therefore, the equation has two distinct real roots.
✦ Try This: Determine the nature of the quadratic equation 8x² + x - 3 = 0.
Given, the equation is 8x² + x - 3 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 8, b = 1 and c = -3
b² - 4ac = (1)² - 4(8)(-3)
= 1 + 96
= 97 > 0
We know that a quadratic equation ax² + bx + c = 0 has 2 distinct real roots when the discriminant of the equation is greater than zero.
Therefore, the equation has 2 distinct real roots
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 1 (vii)
√2x² - 3/√2x + 1/√2 = 0. State whether the following quadratic equation has two distinct real roots
Summary:
Quadratic equations are second-degree algebraic expressions and are of the form ax2 + bx + c = 0. The quadratic equation √2x² - 3/√2x + 1/√2 = 0 has 2 distinct real roots.
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