Question

If A.M and G.M of roots of a Quadratic equation are 8 and 5, respectively then obtain the quadratic equation.​

Answer 1

Answer:

Step-by-step explanation:

Let the root of quadratic equation are α and β

Then,

a.m=a+b/2=8

g.m=root of(a.b)=5

hence,

α + β = 16 and , αβ = 25

now, we know,

a/c to quadratic equation:

the quadratic equation : x² -(sum of root)x + (product of root)

= x² -16x + 25

Hence, x² - 16x + 25 = 0

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

GIVEN :

A.M of roots of Quadratic Equation = 8

G.M of roots of Quadratic Equation = 5

SOLUTION :

Let the roots of the quadratic equation be 'a' and 'b'

A/Q,

A.M of roots of Quadratic Equation = 8

$\sf{ \implies \: \frac{a + b}{2} = 8}$

$\implies \: \sf{a + b = 16} \: \: \rightarrow(1)$

G.M of roots of Quadratic Equation = 5

$\implies \: \sf {\sqrt{ab} \: = \: 5}$

Squaring both sides, we get

$\implies \: \sf{ab = 25} \: \: \rightarrow(2)$

Now, our required Quadratic Equation is

$\implies \: \sf {{x}^{2} - (a + b)x + ab} = 0$

Putting the values from (1) and (2) we get,

$\implies \: \boxed{ \sf{{x}^{2} - 16x + 25} = 0}$