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5x² - 2x - 10 = 0, find whether the equation has real roots. If real roots exist, find them

Solution:

Given, the quadratic equation is 5x² - 2x - 10 = 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 = 5, b = -2 and c = -10

So, b² - 4ac = (-2)² - 4(5)(-10)

= 4 + 200

= 204 > 0

So, the equation has 2 distinct real roots.

By using the quadratic formula,

x = [-b ± √b² - 4ac]/2a

x = (2 ± √204)/2(5)

= (2 ± 2√51)/10

Now, x = (2 + 2√51)/10 = 2(1+√51)/10 = (1+√51)/5

x = (2 - 2√51)/10 = 2(1-√51)/10 = (1-√51)/5

Therefore, the roots of the equation are (1+√51)/5 and (1-√51)/5.

✦ Try This: check whether the equation 9x² + 2x - 11 = 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 (iii)

Summary:

The equation 5x² - 2x - 10 = 0 has real roots which can be written as x = (1-√51)/5 and x = (1+√51)/5

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