8x² + 2x - 3 = 0, find whether the equation has real roots. If real roots exist, find them
Solution:
Given, the quadratic equation is 8x² + 2x - 3 = 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
Here, a = 8, b = 2 and c = -3
So, b² - 4ac = (2)² - 4(8)(-3)
= 4 + 96
= 100 > 0
So, the equation has 2 distinct real roots.
By using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
x = (-2 ± √100)/2(8)
= (-2 ± 10)/16
Now, x = (-2 + 10)/16 = 8/16 = 1/2
x = (-2 - 10)/16 = -12/16 = -3/4
Therefore, the roots of the equation are 1/2 and -3/4
✦ Try This: check whether the equation x² + 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 (i)
8x² + 2x - 3 = 0, find whether the equation has real roots. If real roots exist, find them
Summary:
The equation 8x² + 2x - 3 = 0 has real roots x = 1/2 and x = -¾
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