Question

The parallel and geometric mean of the roots of a quadratic equation is 8 and 5. Find the quadratic equation. ​

Answer 1

Step-by-step explanation:

Let the two roots be α and β

∴

2

α+β

=8 (AM of a and b is

2

a+b

) ⟶(1)

and

αβ

=5 (GM of a and b is

ab

) ⟶(2)

From (1)

α+β=16

⇒ sum of roots =α+β=16

From (2)

αβ

=5

⇒αβ=25

∴ Products of roots =25

Now, we know that if we have the sum of roots and product of roots then the quadratic equation is given by

x

2

− (sum of the roots)x + (product of the roots) =0

∴ the quadratic equation with roots α,β are

x

2

−(α+β)x+αβ=0

x

2

−16x+25=0

Answer 2

Busy ?????????????????