Question

If one root of the quadratic equation x² - 8tx - 25 = 0 is 3 + 4t, then the other root must be:
1. 3 - 4t
2. -3 - 4t
3. 3 + 4t
4. -3 + 4t

Answer 1

Correct Answer - Option 4 : -3 + 4t

Concept:

Consider a quadratic equation:

a² + bx + c = 0

the equations has roots equal to α; B

then \(\alpha + \beta = - \frac{b}{a}\) and \(\alpha \beta = \frac{c}{a}\)

Analysis:

x² – 8tx – 25 = 0

α = 3 + 4t

3 + 4t + β \(= \frac{{8t}}{1}\)

∴ β = 8t – 4t – 3

= 4t – 3