Question

The equation having the roots 3 and 5 is​

Answer 1

SOLUTION

TO DETERMINE

The equation having the roots 3 and 5

CONCEPT TO BE IMPLEMENTED

If the Sum of zeroes and Product of the zeroes of a quadratic equation is given then the quadratic equation is

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

EVALUATION

We have to find the equation having the roots 3 and 5

Since number of roots is 2

So the required equation is a quadratic equation

Now the given roots are 3 and 5

Sum of the roots = 3 + 5 = 8

Product of the roots = 3 × 5 = 15

Hence the required Quadratic equation is

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

$\sf \implies \: {x}^{2} -8x + 15 = 0$

FINAL ANSWER

Hence the required equation

$\sf \: {x}^{2} -8x + 15 = 0$

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