Question

Q1. if one root 3 times the other of eq. ax^2+bx+c=0, then find b:ac


Q2.is 2 a root of the equation x^2+3x-12=0



urgent

Answer 1

1)

ax² + bx + c =0

Let the first root of this equation be x

according to question second root = 3x

We know sum of roots = – b / a

x + 3x = – b / a

4x = – b / a

x = – b / 4a

also product of roots = c / 4

x ( 3x) = c / 4

3x² = c / 4

x² = c / 12

x = √c / 2√3

equating x

– b / 4a = √c / 2√3

– b / a√c = 4 / 2√3

b / a√c = – 2 √3

2) x² + 3x – 12

To check 2 is the root of equation put x = 2

(2)² + 3 ( 2) – 12

= 4 + 6 – 12

= 10 – 12

= – 2

≠ 0

Hence 2 is not a root of the above equation.