Question

The product of two numbers is 48 and their sum is 16. Express in quadratic equation

Answer 1

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Answer 2

Product = 48

Sum = 16

Let the roots of the quadratic equation be α, β

$\alpha \times \beta = 48 \\ \\ ⇒ \frac{ - b}{a} = 48 \: \: \: \quad \: equation \: 1$

where

b is the x coefficient

a is the x² coefficient.

$\alpha + \beta = \frac{c}{a} \\ \\ \implies 16 = \frac{c}{a} \: \: \: \quad \: equation \: 2$

Now, in the above 2 equations;

Let, a = 1

when you substitute value of a as 1 in equation 1,

⇒ b = -48

Similarly,

c = 16

Quadratic equation is written in the form

ax² + bx + c.

Substitute value of a, b and c in the above equation.

Therefore, the required quadratic equation is

x² - 48x + 16