Find the value 'p' so that the equation 4x2−8px+9=0 has roots whose difference is 4.

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Filo · Accepted Answer

We know that if m and n are the roots of a quadratic equation ax2+bx+c=0, the sum of the roots is m+n=−ab​ and the product of the roots is mn=ac​.Let m and n be the roots of the given quadratic equation 4x2−8px+9=0. It is given that the difference of the roots is 4, therefore,m−n=4........(1)The equation 4x2−8px+9=0 is in the form ax2+bx+c=0 where a=4,b=−8q and c=9.  The sum of the roots is:m+n=−ab​=−4(−8q)​=2q....(2)The product of the roots is ac​ that is:mn=ac​=49​......(3) Now, we know the identity (m+n)2=(m−n)2+4mn, therefore, using equations 1,2 and 3, we have(m+n)2=(m−n)2+4mn⇒(2p)2=42+(4×49​ )⇒4p2=16+9⇒4p2=25⇒p2=425​⇒p=±425​ ​⇒p=±25​   Hence, the value of p=±25​.

Question Text	Find the value 'p' so that the equation $4 x^{2} - 8 p x + 9 = 0$ has roots whose difference is 4.
Answer Type	Text solution:1
Upvotes	150

Find the value 'p' so that the equation $4 x^{2} - 8 p x + 9 = 0$ has roots whose difference is 4.

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