Question

If AmandG.M of roots of a Quadratic eqn are 8 and 5, respectively then obtain the qua equation.​ ​

Answer 1

Answer:

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Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Correct Question :- \: \star}}}}}$

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

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GIVEN :

A.M of roots of Quadratic Equation = 8

G.M of roots of Quadratic Equation = 5

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

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,

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

Hope it helps uhh