Class 10 Math All topics Quadratic Equations

Find the value 'p' so that the equation has roots whose difference is 4.
Solution:
We know that if and are the roots of a quadratic equation , the sum of the roots is  and the product of the roots is .

Let and be the roots of the given quadratic equation . It is given that the difference of the roots is , therefore,

The equation  is in the form  where and .

The sum of the roots is:

The product of the roots is  that is:

Now, we know the identity , therefore, using equations 1,2 and 3, we have

Hence, the value of .

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