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Find the quadratic equation whose roots are \(\frac{2}{3} an...

Find the quadratic equation whose roots are 23and34

A.

12y2y6=0

B.

12y2y+6=0

C.

12y2+y6=0

D.

y2+y6=0

Correct answer is C

Let p = 23 and q =  34

using (y - p)(y - q) = 0

= ( y -  23)( y - (34))=0

 =  (y23)(y+34) = 0

y2+34y23y612=0

y2+112y12 = 0

= multiply through by the l. c. m of 3 and 4 = 12

∴ the quadratic equation is  12y2+y6=0