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

Question

If A.M. and G.M. of roots of a quadratic equation are 8 and 5 , respectively, then quadratic equation is (A) x2+16 x+25=0 (B) x2-16 x-25=0 (C) x2+16 x-25=0 (D) x2-16 x+25=0

Tardigrade Admin · Accepted Answer

Let the roots of the quadratic equation are

α

and

β

, then (arithmetic mean)

\frac{α + β}{2} = 8

and (geometric mean)

α β = 5

\Rightarrow α + β = 16

and

α β = 25

Now, if roots are

α

and

β

, then quadratic equation is

x^{2} -

(sum of roots

) x +

product of roots

= 0

\Rightarrow x^{2} - (α + β) + α β = 0

\Rightarrow x^{2} - 16 x + 25 = 0

Q. If A.M. and G.M. of roots of a quadratic equation are 8 and 5 , respectively, then quadratic equation is

$x^{2} + 16 x + 25 = 0$

$x^{2} - 16 x - 25 = 0$

$x^{2} + 16 x - 25 = 0$

$x^{2} - 16 x + 25 = 0$

Q. If A.M. and G.M. of roots of a quadratic equation are 8 and 5 , respectively, then quadratic equation is

x2+16x+25=0

x2−16x−25=0

x2+16x−25=0

x2−16x+25=0

Let the roots of the quadratic equation are α and β, then (arithmetic mean) 2α+β​=8 and (geometric mean) αβ​=5 ⇒α+β=16 and αβ=25 Now, if roots are α and β, then quadratic equation is x2− (sum of roots )x+ product of roots =0 ⇒x2−(α+β)+αβ=0 ⇒x2−16x+25=0

$x^{2} + 16 x + 25 = 0$

$x^{2} - 16 x - 25 = 0$

$x^{2} + 16 x - 25 = 0$

$x^{2} - 16 x + 25 = 0$