Q) Solve the quadratic equation 2x² – 3x – 5 = 0 using the quadratic formula.

Ans: [Approach: we know that the in a quadratic formula, the value of x is calculated by: x = , where, b² – 4 a c is the discriminant. Hence, if we calculate the value of the discriminant and solve by the above formula, we can get value of x]

Given Quadratic equation is: 2 x² – 3 x – 5 = 0

Step 1: We know that the standard quadratic equation is given by:

a x² + b x + c = 0

By comparing the given quadratic equation with the standard quadratic equation, we get:

a = 2, b = – 3, c = – 5

Step 2: Let’s calculate the discriminant now:

D = b² – 4 a c = (- 3)² – 4 (2) (-5)

= 9 + 40 = 49

Step 3: Let’s solve for x by putting values in the quadratic formula:

x =

x =

Step 4: Since the discriminant is positive, we get two real roots:

Therefore, x = = =

and x = = = – 1

Therefore, the solutions of given quadratic equation are: x = and  x = – 1

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