Option 2 : b^{2} + c^{2} = 2a^{2}

RBI Grade B 2020: Full Mock Test

9431

200 Questions
200 Marks
120 Mins

**Concept:**

If the **quadratic equation** is given by Ax^{2} + Bx + C = 0.

**Then,**

Sum of roots = - \(\frac{B}{A}\)

Product of roots = \(\frac{C}{A}\)

**Given:**

(a2 - b2) x2 + (b2 - c2) x + c2 - a2 = 0

**Where,**

A = (a2 - b2), B = (b2 - c2), C = c2 - a2

**Calculation:**

**Here,**

A + B + C = (a2 - b2) + (b2 - c2) + (c2 - a2) = 0.

So, we can say that** x = 1** is a root of a given quadratic equation.** According to question both roots are same**.

**Then,**

Roots (x) = 1, 1

**Product of Roots** = \(\frac{C}{A}\)

1 × 1 = \(\frac{(c^2~-~a^2)}{(a^2~-~b^2)}\)

(a2 - b2) = (c2 - a2)

**By arranging, we get**

**b ^{2} + c^{2} = 2a^{2}**