# If p, q, r, are real, $p\neq q$, then the roots of the equation $(p-q)x^{2}-5(p+q)x-2(p-q)=0$  are Option 1) Real and equal Option 2) Non real Option 3) Real and unequal Option 4) None of these

P Prateek Shrivastava

As we learnt in

Condition for Real and distinct roots of Quadratic Equation -

$D= b^{2}-4ac> 0$

- wherein

$ax^{2}+bx+c= 0$

$\\( p-q) \right )x^{2}-5\left ( p+q \right )x-2\left ( p-q \right )=0\ \\\\\*\left\[ 5\left ( p+q \right ) \right ]^{2}-4\times \left ( -2 \right )\left ( p-q \right )^{2}\\*\\=25\left ( p+q \right )^{2}+8\left ( p-q \right )^{2}> 0$

Option 1)

Real and equal

Incorrect

Option 2)

Non real

Incorrect

Option 3)

Real and unequal

Correct

Option 4)

None of these

Incorrect

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