Question

form a quadratic equation whose roots are 4 and 7

Answer 1

Quadratic equation = x² -(4+7)x+(4×7)

= x² -11x + 28

Answer 2

The quadratic equation whose roots are 4 and 7 is x² - 11x + 28 = 0

Given :

The roots 4 and 7

To find :

The quadratic equation whose roots are 4 and 7

Concept :

If the roots of a quadratic equation is given then the quadratic equation is

$\sf {x}^{2} -(Sum \: of \: the \: roots )x + Product \: of \: the \: roots = 0$

Solution :

Step 1 of 2 :

Write down the given roots of the quadratic equation

Here it is given that the roots are 4 and 7

Step 2 of 2 :

Find the quadratic equation

The quadratic equation is

$\sf {x}^{2} -(Sum \: of \: the \: roots )x + Product \: of \: the \: roots = 0$

$\sf \implies \: {x}^{2} -(4 + 7 )x + (4 \times 7)= 0$

$\sf \implies \: {x}^{2} -11x + 28= 0$

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