-2x² + 3x + 2 = 0, find whether the equation has real roots. If real roots exist, find them
Solution:
Given, the quadratic equation is -2x² + 3x + 2 = 0
We have to find whether the equation has real roots or not.
A quadratic equation ax² + bx + c = 0 has 2 distinct real roots when the discriminant of the equation is greater than zero.
Discriminant = b² - 4ac
The equation can be rewritten as -(2x² - 3x - 2) = 0
2x² - 3x - 2 = 0
Here, a = 2, b = -3 and c = -2
So, b² - 4ac = (-3)² - 4(2)(-2)
= 9 + 16
= 25 > 0
So, the equation has 2 distinct real roots.
By using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
x = (3 ± √25)/2(2)
= (3 ± 5)/4
Now, x = (3 + 5)/4 = 8/4 = 2
x = (3 - 5)/4 = -2/4 = -1/2
Therefore, the roots of the equation are -1/2 and 2.
✦ Try This: check whether the equation 6x² + 2x - 3 = 0 has real roots. If real roots exist, find them
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 1 (ii)
-2x² + 3x + 2 = 0, find whether the equation has real roots. If real roots exist, find them
Summary:
The equation -2x² + 3x + 2 = 0 has real roots which can be written as x = -1/2 and x = 2
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