Question

If a,b,c ∈Q and p+√q (p,q ∈ Q) is an irrational root of ax+bx+c=0 then the other root is​

Answer 1

Answer:

We have here a quadratic equation. When we find the roots of an equation such as this, we use the quadratic formula:

x = (-b ± √(b2 - 4ac)) / 2a

where a, b, and c are coefficients.

In this equation

a = a

b = -b

c = c

The plus/minus sign indicates that we will have two solutions. Suppose that root p was found using the plus and root q was found using the minus. We will have these roots.

p = (b + √(b2 - 4ac)) / 2a and q = (b - √(b2 - 4ac)) / 2a

Since we want to find the value of p + q, we simply add the formula.

p + q = ((b + √(b2 - 4ac)) + (b - √(b2 - 4ac))) / 2a

The square-root terms cancel each other out.

p + q = 2b / 2a

p + q = b / a

Hope this helps!

Answer 2

Answer:

For the quadratic equation ax

2

+bx+c=0,a,b,c,εQ

Roots are given by

α=

2a

−b+

b

2

−4ac

and

β=

2a

−b−

b

2

−4ac

If D=0 then α=

2a

−b

=β i.e. the roots are equal and real.

Since a,b and c∈Q, the roots will be equal and rational.

Hence, statements P and R are correct.

hope it helps you ✅✅✅