Math, asked by dura35, 11 months ago

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

Answers

Answered by ravi9848267328
6

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


ravi9848267328: ok
Answered by BraɪnlyRoмan
73

\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}


dura35: hii
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