Question

which of the following equation has roots 3 and 5?​

Answer 1

Answer:

Solution. Hence, the correct answer is x2 - 8x + 15 = 0.

Step-by-step explanation:

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Answer 2

The equation with roots 3 and 5 is x² - 8x + 15 = 0

Given :

The roots 3 and 5

To find :

The quadratic equation

Formula :

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

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

Solution :

Step 1 of 2 :

Find sum and product of roots

Here it is given that the quadratic equation has roots 3 and 5

Sum of the roots = 3 + 5 = 8

Product of the roots = 3 × 5 = 15

Step 2 of 2 :

Find the equation

Hence the required Quadratic equation is

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

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

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