Question

from a quadratic equation whose roots are 4 and -7​

Answer 1

The required quadratic equation whose roots are 4 and - 7 is x² + 3x - 28 = 0

Given :

A quadratic equation whose roots are 4 and - 7

To find :

The quadratic equation

Concept :

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

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

Solution :

Step 1 of 2 :

Find Sum of roots and Product of the roots

Here it is given for a quadratic equation whose roots are 4 and - 7

Sum of roots = 4 + ( - 7) = 4 - 7 = - 3

Product of the roots = 4 × ( - 7) = - 28

Step 2 of 2 :

Find the quadratic equation

The required quadratic equation is given by

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

$\displaystyle \sf \implies {x}^{2} - (-3)x + (-28) = 0$

$\displaystyle \sf \implies {x}^{2} +3x - 28 = 0$

Hence the required quadratic equation whose roots are 4 and - 7 is x² + 3x - 28 = 0

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