Question

The quadratic equation 2px^2+qx+7=0,where pand q are constants,has two equal roots.Explain p in terms of q.

Answer 1

@ganeshie8

Answer 2

say the two equal roots are \(\large \rm \alpha , ~\alpha \)

Answer 3

\[\large 2px^2 + qx+7=0\]

dividing through out \(2p\) gives you

\[\large x^2 + \frac{q}{2p}x+\frac{7}{2p}=0\]

Answer 4

since \(\large ~\alpha, \alpha \) are roots, \(\large (x-\alpha)(x-\alpha)\) is a factor, agree ?

Answer 5

agree

Answer 6

you can set them equal :
\[\large x^2 + \frac{q}{2p}x+\frac{7}{2p} = (x-\alpha)(x-\alpha)\]

Answer 7

expand right hand side and compare coefficients both sides