Q7 of 49 Page 1

Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots.

px(x-3) + 9=0


px2-3px + 9=0


This is a quadratic equation of form ax2 + bx + c=0


Where a=p, b=-3p, c=9


For equal roots, D=0


D=b2-4ac=0


Substituting the values of a,b and c


(-3p)2-4(p)(9)=0


⇒ 9p2-36p=0


⇒ 9(p2-4p)=0


⇒ p(p-4)=0


There are two possible values of p, p=0 and p=4


We neglect p=0 as on putting p=0; the equation does not remain quadratic.


∴ p=4 is our required answer.


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