Question

If the mean of two number A and B is 8 and AB =9 ,find the quadratic equation whose roots are A and B

Answer 1

Heya!!


Required quadratic equations in x is

x² - ( A + B )x + ( AB ) = 0


A + B / 2 = 8

A + B = 16

And

AB = 9


x² - ( 16 ) x + 9 = 0


x² - 16x + 9 = 0



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Answer 2

Given:

• The mean of two numbers A and B is 8
• The products of two numbers AB is 9

To Find:

• Identify the quadratic equation.

Solution:

From the given data we can write,

⇒ $\frac{A+B}{2} = 8$  and AB = 9

⇒ A+B = 16 and AB = 9

$ax^2+bx+c=0$ →  (equation 1) is the general form of a quadratic equation.

When the roots of the quadratic equation are A+B and AB, equation 1 becomes,

$x^2+(A+B)x-(AB) = 0$ → (equation 2)

On substituting the values of A+B and AB in equation 2 we get,

$x^2+16-9=0$

∴ The quadratic equation obtained is $x^2+16-9=0$